Self-sustained Wave Research Articles

OPTIMIZATION OF IGNITION ZONE OF ADVANCED FAST REACTOR, WORKING IN NUCLEAR BURNING WAVE MODE

This article deals with the problem of optimizing composition and structure of the ignition zone of the fast reactor operating in the self-sustaining mode of nuclear burning wave with the purpose of its smooth start-up and reducing fissile material amount in initial assembly. The cylindrical homogeneous reactor with the ignition zone placed in the center or near the cylinder end is considered. The analysis has been performed basing on solving the non-stationary neutron diffusion equation together with the fuel burn-up equations and the equations of nuclear kinetics for precursor nuclei of delayed neutrons, with using the radial buckling approximation. An optimized structure of the ignition zone has been proposed, which ensures a smooth transition of the reactor to the self-sustaining nuclear burning wave mode, avoiding an excessive energy release, which is observed when using a simplified scheme of ignition zone. Comparison of the startup variants with the ignition zone at the cylinder end and at its center shows the benefits of the second one.

Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence.

Simulations of elastoinertial turbulence (EIT) of a polymer solution at low Reynolds number are shown to display localized polymer stretch fluctuations. These are very similar to structures arising from linear stability (Tollmien-Schlichting modes) and resolvent analyses, i.e., critical-layer structures localized where the mean fluid velocity equals the wave speed. Computations of self-sustained nonlinear Tollmien-Schlichting waves reveal that the critical layer exhibits stagnation points that generate sheets of large polymer stretch. These kinematics may be the genesis of similar structures in EIT.

Role of Molecular Disorder on the Reactivity of RDX

Shock initiation of heterogeneous high-energy materials is often preceded by the loss of crystalline order around hotspots where mechanical energy is localized and chemical reactions start. We use molecular dynamics (MD) simulations with the reactive force field ReaxFF to determine the impact of molecular disorder on the reactivity of the high-energy material RDX under fast homogeneous heating and hotspots. Under fast heating to identical temperatures, amorphous samples exhibit faster decomposition and reaction than their crystalline counterparts. Following heating, the crystalline samples undergo fast endothermic processes associated with the loss of crystalline order that occur in timescales shorter than chemical decomposition and reduce the actual temperature of the reaction. Once this process is accounted for and actual decomposition temperatures are determined, both amorphous and crystalline samples follow identical kinetics. We also characterize the critical temperature required for a hotspot 10 nm in diameter to become critical and turn into a deflagration wave. In both crystalline and amorphous samples, hotspots with initial temperatures of 1650 K and higher result in self-sustained deflagration waves and those at 1600 K quench. We observe slightly faster propagation in the amorphous samples with initial velocities increasing with temperature. The higher reactivity of amorphous samples is not large enough to explain the significantly increased reactivity in hotspots formed after shock-induced pore collapse observed recently in large-scale MD simulations.

Controlling excitable wave behaviors through the tuning of three parameters.

Excitable systems are a class of dynamical systems that can generate self-sustaining waves of activity. These waves are known to manifest differently under diverse conditions, whereas some travel as planar or radial waves, and others evolve into rotating spirals. Excitable systems can also form stationary stable patterns through standing waves. Under certain conditions, these waves are also known to be reflected at no-flux boundaries. Here, we review the basic characteristics of these four entities: traveling, rotating, standing and reflected waves. By studying their mechanisms of formation, we show how through manipulation of three critical parameters: time-scale separation, space-scale separation and threshold, we can interchangeably control the formation of all the aforementioned wave types.

Origin of Elastic–Plastic Deformation Invariant

We consider the autowave mechanism of evolution of a localized plastic deformation of crystalline solids of different origins. It is found that localization of the plastic flow is determined by the relation between elastic and plastic phenomena in deforming materials. It is shown that the main parameter of deformation processes is the elastic–plastic deformation invariant, viz., a dimensionless quantity connecting quantitatively the parameters of elastic waves and self-sustained waves (autowaves) of localized plastic deformation. The correctness of this statement is verified for metals, alkali-halide crystals, and rocks. The physical origin of the invariant is explained on the basis of thermodynamic considerations.

Self-sustained exothermal waves in amorphous and nanocrystalline films: A comparative study

A comparative experimental study of self-sustained exothermal waves in electrodeposited amorphous antimony (Sb) films, quenched glassy copper-titanium (CuTi) alloy, and magnetron deposited multilayer nickel-aluminum (Ni/Al) films was accomplished using a single approach. It is shown that self-propagating thermal waves can be initiated in all three systems, which convert the amorphous or multilayer metallic structure into nanocrystalline materials. The normalized temperature-time profiles allow us to make a conclusion on the similarity of the processes, despite the diverse driving forces in the considered systems. Periodic microstructures, probably induced by thermal oscillations of the crystallization waves, were observed in Sb and CuTi samples and discussed from the viewpoints of theoretical models.

The build-up and characterization of nuclear burn-up wave in a fast neutron multiplying medium

A study has been carried out on the build-up and characterization of nuclear burn-up wave in fast neutron multiplying media. The focus of the study is more on the transient part of the burn-up wave though the steady state is also studied. The characteristics of the transient part are expressed in terms of new parameters, i.e., Transient Length (TL) and Transient Time (TT) elapsed in establishing the asymptotic burn-up wave. The TT and TL are defined, respectively, as the time and length needed to establish 95% and 99% of the asymptotic neutron flux propagating in the media. From these parameters, the transient wave velocity is determined. The characteristics of asymptotic part of the wave are determined in terms of wave velocity, Full Width at Half Maximum (FWHM) and Full Width at 10% Maximum (FW10M) of neutron flux distribution in the space. A parametric study is also carried out to investigate the sensitivity of these parameters to some of the physical parameters of the ignition zone and the breeder zone of the reactor. The characterization parameters would be very meaningful to understand the transient characteristics of the self-sustaining nuclear burn-up wave and in evaluating the quality of the wave by the researchers working in the field of nuclear burn-up wave build-up and propagation.

Investigation of shock–acoustic-wave interaction in transonic flow

The buffet flow field around supercritical airfoils is dominated by self-sustained shock wave oscillations on the suction side of the wing. Theories assume that this unsteadiness is driven by an acoustic feedback loop of disturbances in the flow field downstream of the shock wave whose upstream propagating part is generated by acoustic waves. Therefore, in this study, first variations in the sound pressure level of the airfoil’s trailing-edge noise during a buffet cycle, which force the shock wave to move upstream and downstream, are detected, and then, the sensitivity of the shock wave oscillation during buffet to external acoustic forcing is analyzed. Time-resolved standard and tomographic particle-image velocimetry (PIV) measurements are applied to investigate the transonic buffet flow field over a supercritical DRA 2303 airfoil. The freestream Mach number is $$M_{\infty } = 0.73$$ , the angle of attack is $$\alpha = {3.5}^{\circ }$$ , and the chord-based Reynolds number is $$Re_c = 1.9\times 10^6$$ . The perturbed Lamb vector field, which describes the major acoustic source term of trailing-edge noise, is determined from the tomographic PIV data. Subsequently, the buffet flow field is disturbed by an artificially generated acoustic field, the acoustic intensity of which is comparable to the Lamb vector that is determined from the PIV data. The results confirm the hypothesis that buffet is driven by an acoustic feedback loop and show the shock wave oscillation to directly respond to external acoustic forcing. That is, the amplitude modulation frequency of the artificial acoustic perturbation determines the shock oscillation.

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.

Exploring the role of inhibitory coupling in duplex networks**Project supported by the National Natural Science Foundation of China (Grant Nos. 11565005 and 11365003).

The electrical coupling of myocytes and fibroblasts can play a role in inhibiting electrical impluse propagation in cardiac muscle. To understand the function of fibroblast–myocyte coupling in the aging heart, the spiral-wave dynamics in the duplex networks with inhibitory coupling is numerically investigated by the Bär–Eiswirth model. The numerical results show that the inhibitory coupling can change the wave amplitude, excited phase duration and excitability of the system. When the related parameters are properly chosen, the inhibitory coupling can induce local abnormal oscillation in the system and the Eckhaus instability of the spiral wave. For the dense inhibitory network, the maximal decrement (maximal increment) in the excited phase duration can reach 24.3%(13.4%), whereas the maximal decrement in wave amplitude approaches 28.1%. Upon increasing the inhibitory coupling strength, the system excitability is reduced and even completely suppressed when the interval between grid points in the inhibitory network is small enough. Moreover, the inhibitory coupling can lead to richer phase transition scenarios of the system, such as the transition from a stable spiral wave to turbulence and the transition from a meandering spiral wave to a planar wave. In addition, the self-sustaining planar wave, the unique meandering of spiral wave and inward spiral wave are observed. The physical mechanisms behind the phenomena are analyzed.

Hydrodynamics of storage release during river ice breakup

The breakup of the ice cover in cold-region rivers is a brief but seminal period of their hydrologic regime, with important ecological and socio-economic implications. The main driver of ice breakup processes is the flow discharge hydrograph. It is generated by runoff from snowmelt and rainfall but can be modified by rapid release of water from storage as the ice cover recedes by ablation and mechanical breaking up. Despite its potential importance, there is very limited quantitative information concerning the hydrodynamic processes that control storage release during ice breakup in rivers, while the issue of climate change underscores the need for improved understanding of the relevant mechanisms. Quantitative analysis for assumed prismatic channels shows that ablation and sustained ice dislodgment and breaking can cause significant flow enhancement via storage release. The latter process is far more dynamic than ablation and, under certain conditions, may lead to formation of a self-sustaining wave (SSW). Analytical results are applied to natural stream conditions, using the Lower Peace River as a case study. Observed rates of ice recession typically indicate ice melt as the dominant process. A rare occurrence of rapid ice breaking over hundreds of kilometres (2014) indicated partial agreement with the SSW concept and revealed that discrepancies may arise from the characteristic irregularity of rivers. Impacts on storage release by climate-driven changes to river ice regimes are examined, along with their implications to ice-jam formation and associated flooding.

Frozen fronts selection in flow against self-sustained chemical waves

Autocatalytic reaction fronts between two reacting species in the absence of fluid flow propagate as solitary waves. The coupling between an autocatalytic reaction front and a forced hydrodynamic flow may lead to a stationary front whose velocity and shape depend on the underlying flow field. We focus on the chemohydrodynamic opposition between forced advection and self-sustained chemical waves, which can lead to static stationary fronts, i.e., frozen fronts (FFs). Toward that end, we perform experiments, analytical computations, and numerical simulations with the autocatalytic iodate-arsenious acid reaction (IAA) over a wide range of flow velocities around a solid disk. For the same set of control parameters, we observe two types of frozen fronts: an upstream FF, which avoids the solid disk, and a downstream FF with two symmetric branches emerging from the solid disk surface. We map the range over which we observe these frozen fronts. We also address the relevance of the so-called eikonal, thin front limit to describe the observed fronts and select the frozen front shapes.2 MoreReceived 29 September 2016DOI:https://doi.org/10.1103/PhysRevFluids.2.043302©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasPatterns in complex systemsReacting flowsTechniquesChemical wavesFluid Dynamics

Microstructure evolution and self-propagating reactions in Ni-Al nanofoils: An atomic-scale description

Abstract The relation microstructure/process in the case of self-propagating reactions in Ni-Al nanofoils was investigated by means of molecular dynamics simulations. We studied the possibility of a stationary self-sustaining reactive wave while varying the initial temperature (from 300 to 800 K) and stoichiometry (from 0.35 to 0.77 of Ni mole fraction). The main features of the wave propagation were obtained. The products of the reaction, and their microstructure along the sample after the passage of the front were described. Along with the formation of a melted alloy Ni-Al at high temperatures, the crystallized intermetallic compound B 2 -NiAl was observed. Two formation mechanisms of B 2 -NiAl were identified: dissolution-precipitation and rapid crystallization from melts. The present study proves that the microstructure differs widely according to the stoichiometry and initial temperature.

Analysis of self-propagating intermetallic reaction in nanoscale multilayers of binary metals

Nanoscale multilayers of two different metals could exhibit super-fast intermetallic reaction wave that accompanies high level of exothermic heat release, while additional advantage is a very small ignition delay. They could be a promising candidate for the core technology in realizing micron-sized initiation device for explosives detonation or propellants ignition in various defense and civilian applications. This numerical investigation focuses on the numerical modeling and computations of the ignition and self-propagating reaction behaviors in nanoscale intermetallic multilayer structures made of alternating binary metal layers of boron and titanium. Due to thin film nature of metallic multilayers, intermetallic reaction propagation across the repeating bimetallic multilayers is approximated to the one-dimensional transient model of thermal diffusion and atomic species diffusion, and the intermetallic reaction between two metal species is assumed to follow Arrhenius dependence on temperature. The computational results show the details of ignition and propagation characteristics of intermetallic reaction wave by evaluating and discussing the effects of key parameters, such as multilayer thickness, excess of one metal species, and presence of atomic premixing at interface of boron and titanium layers, on ignition delay and propagation speed of self-sustaining reaction wave.

Fast propagation regions cause self-sustained reentry in excitable media

Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.

Modeling self-sustaining waves of exothermic dissolution in nanometric Ni-Al multilayers

The self-sustained propagating reaction occurring in nanometric metallic multilayers was studied by means of molecular dynamics (MD) and numerical modeling. We focused on the phenomenon of the exothermic dissolution of one metallic reactant into the less refractory one, such as Ni into liquid Al. The exothermic character is directly related to a negative enthalpy of mixing. An analytical model based on the diffusion-limited dissolution [1] coupled with heat transfer was derived to account for the main aspects of the process. Together, several microscopic simulations were carried out. The first series were set up to obtain all the parameters governing the process, including the heat release by dissolution. The second series of MD simulations was set up to detect the very possibility of self-sustaining propagation driven by exothermic dissolution. We aimed at developing a consistent multiscale description by numerically solving the model with the MD extracted parameters. The study proves that the exothermic intermixing of Ni and Al is a driving mechanism of self-sustaining propagation in reactive nanofoils.

A theory for steady and self-sustained premixed combustion waves

AbstractBased on the compressible Navier–Stokes equations for reactive flow problems, an eigenvalue problem for the steady and self-sustained premixed combustion wave propagation is developed. The eigenvalue problem is analytically solved and a set of analytic formulae for description of the wave propagation is found out. The analytic formulae are actually the exact solution of the eigenvalue problem in the form of integration, based on which author develops an iterative and numerical algorithm for calculation of the steady and self-sustained premixed combustion wave propagation and its speed. In order to explore the mathematical model and test the computational method developed in this paper, three groups of combustion wave propagation modes are calculated. The computational results show that the non-trivial modes of the combustion wave propagation exist and their distribution is not continuous but discrete.

Exothermic Self-Sustained Waves with Amorphous Nickel

The synthesis of amorphous Ni (a-Ni) using a liquid-phase chemical reduction approach is reported. Detailed structural analysis indicates that this method allows for efficient fabrication of high surface area (210 m2/g) amorphous Ni nanopowder with low impurity content. We investigated the self-propagating exothermic waves associated with crystallization of Ni from the amorphous precursor. Time-resolved X-ray diffraction indicates that amorphous nickel crystallizes in the temperature range 445–480 K. High-speed infrared imaging reveals that local preheating of compressed a-Ni nanopowder triggers a self-sustaining crystallization wave that propagates with velocity ∼0.3 mm/s. The maximum temperature of crystallization wave depends on the sample density and can be as high as 600 K. The Kissinger approach is used to determine the apparent activation energy (55.4 ± 4 kJ/mol) of crystallization. The self-diffusion activation energy of Ni atoms in a-Ni is ∼60 kJ/mol, determined through molecular dynamics (MD) si...

Controlling spiral wave and spatiotemporal chaos in cardiac tissues by slowing sodium channel activation and inactivation

Much evidence shows that the appearance and instability of the spiral wave in cardiac tissue can be linked to a kind of heart disease. Therefore there needs a method of controlling spiral wave more safely and effectively. The intelligent modification of specific ion channel to achieve desired control is the future direction of gene therapy in heart disease. The key question that has to be answered is which ion channel is the best candidate for controlling spiral wave. Modern biological technology has been able to make the mutation of sodium channel gene to change its relaxation time constant. In this paper, we adopt the Luo-Rudy phase I model to investigate how to regulate the relaxation time constant of sodium channel gate to control spiral wave and spatiotemporal chaos in cardiac tissues. We suggest a control strategy which slows down the rate of sodium current activation and inactivation by increasing the relaxation time constant of the sodium activation gate by up to times while its fast inactivation gate is clamped to 0.77. Numerical simulation results show that a gradual increase of will cause the activation gate of sodium current to reach maximum more slowly, and its amplitude is gradually reduced, so that the amplitude and duration of the action potential of cardiomyocyte are gradually reduced. When the factor is large enough, the spiral wave and spatiotemporal chaos cannot propagate in the medium except planar wave with low frequency. The reason is that the excitabilities of medium and wave speed significantly decrease. Therefore, the spiral waves and spatiotemporal chaos can be effectively eliminated when the control time is properly selected and the factor is large enough. Spiral wave and spatiotemporal chaos disappear mainly due to conduction obstacle. In some cases, spiral wave can disappear through the transition from spiral wave to target wave or tip retraction. Spatiotemporal chaos disappears after spatiotemporal chaos has evolved into meandering spiral wave. When the parameters are chosen properly, the phenomenon that spiral wave evolves into a self-sustained target wave is also observed. The corresponding target wave source is the pair of spiral waves with opposite rotation directions. These results can provide useful information for gene therapy in heart disease.

Parallel Simulation of Scroll Wave Dynamics in the Human Heart Using the FEniCS Framework

In the heart, scroll waves are three-dimensional self-sustaining spiral waves of electrical excitation. They arise only in pathology and underlie dangerous arrhythmias. Computer simulation of human cardiac arrhythmias is time-consuming and requires parallel computing. In addition, heart simulation is a complicated multilevel task (cell, tissue, organ); parallel multilevel simulation codes are difficult to create and maintain. Here we present an approach to parallel simulation of scroll waves in the left ventricle of the human heart utilizing the FEniCS framework, which allows developing software using near-mathematical notation and provides automatic parallelization. We used the Aliev–Panfilov cell model of heart electrical activity and studied the scalability of FEniCS implementation on parallel computing systems.