Processes In Nuclear Reactors Research Articles

NEUTRON POINT KINETICS MODEL WITH A DISTRIBUTED-ORDER FRACTIONAL DERIVATIVE

In this paper, the solutions of an extended form of the Fractional-order Neutron Point Kinetics (FNPK) equation in terms of Caputo-time derivatives of the same order are investigated. Instead of using a Caputo derivative, a distributed-order fractional derivative in the Caputo sense was employed in the term of the FNPK equation which is multiplied by the reactivity. This term plays an important role in the description of neutron kinetics during the start-up, shutdown, and steady-state processes in nuclear reactors. The extended (DFNPK) model was solved using the beta, normal, bimodal and Dirac delta distributions to investigate their effect on the transient state solutions of the neutron density. Regardless of the distribution used, the most significant finding is that a destabilizing effect on the neutron density is induced when the mode (or the instant of application of the Dirac delta) of the distribution tends to one while maintaining the orders of the Caputo-time derivatives constant. What defines the destabilizing effect are large magnitude oscillations, a rapid decay, and an oscillation-free steady state with a monotonic increase that is parallel to but somewhat above the trend determined by the FNPK equation. The extended model is anticipated to be effective for modeling neutron density dispersion in a highly heterogeneous medium that may be described using distributed derivatives.

Гетерофазные явления при фракционировании трития в водных системах

Tritium is the only one of the radioactive isotopes that a filtering system is unable to neutralize. It is produced by collateral fission processes in nuclear reactors and displays itself in radioactive wastes and effluents in different forms of tritium oxides. Thus the development and application of nuclear energy entails a challenging problem of treating tritium-containing radioactive wastewater. The paper deals with tritium water isotopologues, namely, with prototritium water and deuterotritium water. Various approaches to the problem of tritium separation have been outlined. The choice of the appropriate process of water detritiation depends, first of all, on whether the detritiated water is recycled back to the reactor system or is discharged to the environment and on whether molecular tritium is to be extracted for further application. Special attention is paid to the process of electrosonochemical water detritiation which is shown to be the preferential one due to its ability to provide molecular tritium. Tritiated water decomposition should be preceded by its concentrating, the latter being two-stage and including water conditioning followed by providing concentrated tritiated water. Reverse-osmosis conditioning and salt rectification are considered as preferential techniques.

On the concept of “effective delayed neutron fraction”

The article considers methodological issues related to the conceptual and terminological apparatus of the dynamics of nuclear reactors. Based on an elementary analysis of the standard point reactor kinetics equations, the author shows that it is necessary to clarify the physical meaning of the parameter β included in the equations, which is traditionally interpreted as the “effective delayed neutrons fraction” (EDNF). It follows directly from the kinetics equations that the parameter β, which appears in these equations as the EDNF, is, from the point of view of the neutron balance, the fraction of prompt neutrons consumed for the generation of delayed neutron precursors (DNPs), and, from the point of view of the DNP balance, the DNP yield per prompt neutron in a single fission event. With these interpretations taken into account, the role of the β parameter is considered in situations related with its adjustment by multiplying it by the “delayed neutron efficiency factor” and with the establishment of the actual fractions of prompt and delayed neutrons. In particular, it is shown that: the statement “if the delayed neutron fraction is β, then the prompt neutron fraction is equal to 1 – β”, used in the problems of analyzing the nuclear reactor dynamics as a starting position, cannot be considered applicable to any reactor conditions; an increase in the β parameter by multiplying it by the “delayed neutron efficiency factor” leads, contrary to traditional interpretations, not to an increase but to a decrease in neutron reproduction in a supercritical reactor. The proposed clarifications are appropriate both in terms of more adequate descriptions of processes in nuclear reactors and in relation to the formulations of nuclear safety requirements.

Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative

Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter β,γ→1, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations.

Remove Liquid Radioactive Wastes Utilizing Nanofiltration, Ultrafiltration, and Microfiltration Membranes

Radioactive waste is generated from fuel cycle processes in nuclear reactors and nuclear power plants (NPPs) in electrical power production, radioisotope manufacturing in nuclear research centers, and medical, industrial, and agricultural applications. Also, natural chain-linked radioisotopes (NORM) are generated from processing and burning fossil fuels and producing oil and natural gas. Therefore, a planned and integrated radioactive waste management strategy must be adopted to protect human health and the environment from the dangers of this waste through published research on a comprehensive radioactive waste management strategy and the testing and dissemination of several treatment options. The main objective is to draw the scientific community's attention to the possibility of using pressure-driven membrane separation in treating radioactive wastewater compared to conventional methods. This short review addresses developments in the treatment and removal of radioactive effluents (LRWs) by pressure-driven membrane methods and improvements in routine treatment of dissolved radioactive ions by chemical treatment of the feed solution followed by membrane separation. Also, recent advances in treating radioactive waste use nanoparticles (NPs) incorporated in polymeric membranes.

STUDY OF XENON POWER FLUCTUATIONS IN WWER-1000 REACTORS IN ONE-DIMENSIONAL AXIAL GEOMETRY

The article uses the adiabatic modelling method for slow transient processes in nuclear reactors. The essence of this method is that the spatial component of the neutron flux density is determined by the solution of static equations of neutron transport. And the time dependence is reduced to the change of parameters (neutron interaction cross-section) of neutron transport equations accordingly to the change of 135Xe, 149Sm concentrations.
 In this work, we propose to use a unidimensional (axial) model in the two-group diffusion approximation to investigate xenon transients. As a result, the effect of delayed neutrons in this case may be overlooked. All neutrons are assumed to be instantaneous because the lifetime of both instantaneous and delayed neutrons is much shorter compared to the characteristic time of the xenon transition process. The diffusion equation is based on a balance equation in which the generation, absorption, and leakage of neutrons per unit core volume determine the rate of change in neutron density over time. The differential equations used to calculate the spatio-temporal behavior of the neutron field in the core volume are calculated numerically, by finite-difference method, and analytically. The neutron-physical constants of each axial layer are determined by averaging, taking into account the number and types of fuel assemblies in accordance with the loading of the core in question. The fuel assembly type constants are preliminarily calculated using spectral codes.
 As a result of the work, an algorithm for the physical calculation of the WWER 1000 reactor in one-dimensional axial geometry was obtained, the validation of the developed program was carried out, a number of transient calculations were carried out and a variety of xenon transient optimizations were proposed.

Upscaling and downscaling the heat transfer process coupled with neutronic reflected core for sodium-cooled fast nuclear reactor

The heat transfer phenomena are crucial in nuclear reactors' design and safety analysis due to the feedback effects with the neutronic processes for power generation. Nuclear reactors are heterogeneous systems containing hundreds of thousands of fuel pins that exhibit power distribution through the space, and the temperatures between the coolant fluid and pins are different. This work analyzes the heat transfer process in liquid metal-cooled fast nuclear reactors with two upscaled energy equations based on the volume averaging method, which is widely applied for the analysis of transport in multiphase systems. The upscaled heat transfer model is coupled with a neutronic reflected core model including feedback effects from the nuclear fuel and liquid metal temperatures. The coupled mathematical models are employed within a called downscaling procedure, which represents a novel methodology with scopes beyond conventional problems in heat transport processes in nuclear reactors. The downscaling process allows us to increase the degree of resolution in the reactor core since this considers the scale of the fuel assembly and that of individual pins at the smallest scale, i.e. a single fuel pin surrounded by liquid metal. This point is crucial for analyzing hot spots in the reactor core.

Multiscale model reduction for neutron diffusion equation

Modelling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The neutron diffusion approximation is widely used for reactor analysis and applied in most engineering calculation codes. In this paper, we attempt to employ a model reduction technique based on the multiscale method for neutron diffusion equation. The proposed method is based on the use of a generalized multiscale finite element method. The main idea is to create multiscale basis functions that can be used to effectively solve on a coarse grid. From calculation results, we obtain that multiscale basis functions can properly take into account the small-scale characteristics of the medium and provide accurate solutions. The results calculated with the GMsFEM are compared with the reference fine-grid calculation results.

Numerical Approximation for Fractional Neutron Transport Equation

Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.

Design Implementation and Parallel Operation of High-Current High-Power Multipulse Converters Feeding Nuclear Fuel Simulators

Nuclear reactors are designed to maintain a chain reaction producing a steady flow of neutrons generated by fission of heavy nuclei, such as uranium. They produce thermal energy, which is converted into mechanical energy and ultimately into electrical energy feeding to a grid network. In a nuclear reactor, fuel undergoes various power/temperature transients during normal and off -normal situations. One needs to simulate these transients in experimental facilities for performing variety of reactor engineering and safety related tasks. The facility consists of scaled thermal hydraulic test setup comprising process equipment, instrumented nuclear fuel channel simulator, and high current converters for feeding power equivalent to fission power to those simulators to handle the transients safely in controlled manner. The experimental results are used to generate database of various vital nuclear reactor process parameters under all types of operational transients and off -normal conditions that can be compared with predictions from computer codes thus validating ever-evolving and advanced software. Besides, simulation of severe accidental conditions of nuclear reactor in facility is also necessary for evaluation of thermal hydraulic design safety margin. A low-resistance fuel simulator of identical geometry with power scaling is directly heated by high dc current to simulate fission power for generating experimental database. The converters have capability to generate power/temperature transients for simulating nuclear reactor conditions. This article presents design, functional description, specifications, simulation, hardware implementation of 10 kA, 12-pulse, thyristorized converters powering fuel simulators. The successful implementation of parallel operation of four converters feeding 27 kA current is described in this article.

“Acid spike” formation in the fast neutron radiolysis of supercritical water at 400 °C studied by Monte Carlo track chemistry simulations

A reliable understanding of radiolysis processes in supercritical water (SCW) cooled reactors is required to ensure optimal water chemistry control. In this perspective, Monte Carlo track chemistry simulations of the radiolysis of pure, deaerated SCW at 400 °C by 2 MeV mono-energetic neutrons were carried out as a function of water density between 0.15 and 0.6 g/cm3. The yields of hydronium ions (H3O+) formed at early time were obtained based on the G values calculated for the first three generated recoil protons. Combining our calculated G(H3O+) values with a cylindrical track model allowed us to estimate the concentrations of H3O+ and the corresponding pH values. An abrupt, transient, and highly acidic pH response (“acid spikes”) was observed at early times around the “native” fast neutron and recoil proton trajectories. This intra-track acidity was found to be strongest at times of less than a few tens to a hundred of picoseconds, depending on the value of the density considered (pH ∼ 1). At longer times, the pH gradually increased for all densities, finally reaching a constant value corresponding to the non-radiolytic, pre-irradiation concentration of H3O+, due to the autoprotolysis of water. Interestingly, the lower the density of the water, the longer the time required to reach this constant value. Because many in-core processes in nuclear reactors critically depend on the pH, the present work raises the question whether such highly acidic pH fluctuations, though local and transitory, could promote or contribute to corrosion and degradation of materials under proposed SCW-cooled reactor operating conditions.

State change modal method for numerical simulation of dynamic processes in a nuclear reactor

Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modelled by a successive change of the reactor states, which are characterized by given coefficients of the equations. In the modal method, the approximate solution is represented as an expansion on the first eigenfunctions of some spectral problem. The numerical-analytical method is based on the use of the dominant time-eigenvalues of a multigroup diffusion model taking into account delayed neutrons. In this work, the application of the modal methodology based on calculation of the dominant eigenvalues and eigenfunctions of α-eigenvalue problem has been tested for the VVER-1000 reactor test model. The last is characterized by the fact that some eigenvalues are complex. Reactor dynamics behavior is simulated for symmetrical and non-symmetrical control rods insertion/withdrawal. The power calculation results obtained with the modal method were compared with the numerical solution of the dynamics problem. A rather good agreement was shown for the problem with single delayed neutron precursor group.

Modelling dynamic processes in a nuclear reactor by state change modal method

Modelling of dynamic processes in nuclear reactors is carried out, mainly, using the multigroup neutron diffusion approximation. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modelled by a successive change of the reactor states. It is considered that the transition from one state to another occurs promptly. In the modal method the approximate solution is represented as eigenfunction expansion. The numerical-analytical method is based on the use of dominant time-eigenvalues of a group diffusion model taking into account delayed neutrons.

On some control problems of dynamic of reactor

The paper analyzes controllability of the transient processes in some problems of nuclear reactor dynamics. In this case, the mathematical model of nuclear reactor dynamics is described by a system of integro-differential equations consisting of the non-stationary anisotropic multi-velocity kinetic equation of neutron transport and the balance equation of delayed neutrons. The paper defines the formulation of the linear problem on control of transient processes in nuclear reactors with application of spatially distributed actions on internal neutron sources, and the formulation of the nonlinear problems on control of transient processes with application of spatially distributed actions on the neutron absorption coefficient and the neutron scattering indicatrix. The required control actions depend on the spatial and velocity coordinates. The theorems on existence and uniqueness of these control actions are proved in the paper. To do this, the control problems mentioned above are reduced to equivalent systems of integral equations. Existence and uniqueness of the solution for this system of integral equations is proved by the method of successive approximations, which makes it possible to construct an iterative scheme for numerical analyses of transient processes in a given nuclear reactor with application of the developed mathematical model. Sufficient conditions for controllability of transient processes are also obtained. In conclusion, a connection is made between the control problems and the observation problems, which, by to the given information, allow us to reconstruct either the function of internal neutron sources, or the neutron absorption coefficient, or the neutron scattering indicatrix....

Linear inverse problem of the reactor dynamics

The aim of this work is the study transient processes in nuclear reactors. The mathematical model of the reactor dynamics excluding reverse thermal coupling is investigated. This model is described by a system of integral-differential equations, consisting of a non-stationary anisotropic multispeed kinetic transport equation and a delayed neutron balance equation. An inverse problem was formulated to determine the stationary part of the function source along with the solution of the direct problem. The author obtained sufficient conditions for the existence and uniqueness of a generalized solution of this inverse problem.

Spectral properties of dynamic processes in a nuclear reactor

As a rule, mathematical modeling of dynamic processes in nuclear reactors is conducted using an approach that treats a neutron flux in the multigroup diffusion approximation. In this approach, the basic model involves a multidimensional system of coupled parabolic-type equations. Similarly to common thermal phenomena, it is possible here to separate a regular mode of nuclear reactor operation that is associated with a selfsimilar development of a neutron field at large times. In this case, the main feature of dynamic processes is a minimal eigenvalue of the corresponding spectral problem. In the present paper, calculations of various eigenvalues are performed via the two-group model and discussed for the VVER-1000 reactor without a reflector and HWR reactor.

Current state of system thermohydraulic codes and trends in their development abroad

The current tendencies in development of the system thermohydraulic codes for analysis of emergency processes in nuclear reactor cooling systems abroad are considered. The main trends towards improvement of physical models, numerical methods, and the code architecture and their validation are reported. Works on the techniques for evaluation of the uncertainty of the calculation results obtained using the thermohydraulic codes are listed.

Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

The singularly perturbed method (SPM) is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power) and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power) and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

Study on Neutron Energy Spectrum in the TMSR

Neutron energy spectrum has a high correlation with all kinds of nuclear processes in nuclear reactor. Neutron energy spectrums of the TMSR in some conditions were simulated using MCNP5.The distributions of thermal neutrons, epithermal and resonance neutrons, and fast neutrons in axial and radial were simulated, respectively. The simulation results indicate that thermal neutrons have a high ratio and control rods inserting the nuclear reactor have a serious effect on neutron distribution. The study of neutron energy spectrum is theoretical basis for measurement in the TMSR.

Optimization of xenon transient processes in nuclear reactors

Optimization of xenon transient processes in nuclear reactors