Direct Numerical Modeling Research Articles

Direct numerical simulation of turbulent, generalized Couette–Poiseuille flow

We present direct numerical simulation (DNS) and modelling of incompressible, turbulent, generalized Couette–Poiseuille flow. A particular example is specified by spherical coordinates $(Re,\theta,\phi )$ , where $Re = 6000$ is a global Reynolds number, $\phi$ denotes the angle between the moving plate, velocity-difference vector and the volume-flow vector and $\tan \theta$ specifies the ratio of the mean volume-flow speed to the plate speed. The limits $\phi \to 0^\circ$ and $\phi \to 90^\circ$ give alignment and orthogonality, respectively, while $\theta \to 0^\circ,\ \theta \to 90^\circ$ correspond respectively to pure Couette flow in the $x$ direction and pure Poiseuille flow at angle $\phi$ to the $x$ axis. Competition between the Couette-flow shear and the forced volume flow produces a mean-velocity profile with directional twist between the confining walls. Resultant mean-speed profiles relative to each wall generally show a log-like region. An empirical flow model is constructed based on component log and log-wake velocity profiles relative to the two walls. This gives predictions of four independent components of shear stress and also mean-velocity profiles as functions of $(Re,\theta,\phi )$ . The model captures DNS results including the mean-flow twist. Premultiplied energy spectra are obtained for symmetric flows with $\phi =90^\circ$ . With increasing $\theta$ , the energy peak gradually moves in the direction of increasing $k_x$ and decreasing $k_z$ . Rotation of the energy spectrum produced by the faster moving velocity near the wall is also observed. Rapid weakening of a spike maxima in the Couette-type flow regime indicates attenuation of large-scale roll structures, which is also shown in the $Q$ -criterion visualization of a three-dimensional time-averaged flow.

Теоретические основы оценки аэродинамического воздействия ветровых потоков на сооружения завода по подготовке и сжижению природного газа

Leaks (spills) of liquefied gases evaporate rapidly on the ground (water) and initially generate a cold plume of heavy vapors. The plume spreads fast downwind, heats up with time, and can become positively volatile in case the concentration of interest for the study (above the lower flammability limit) is reached; therefore, the plume can rise and transform into a vapor cloud. The plume or the vapor cloud can ignite in the flash form. Such situations are possible at liquefied natural gas production plants or regasification units where large amounts of explosive substances are handled involving changes in their aggregate state. The article analyses the significance of the wind impact on the facilities of natural gas liquefaction plants for regular operation and the potential consequences of emergencies. In order to assess the wind impact, the direct numerical modeling of the structure of local wind flows generated at the airflow around the plant facilities by vertical method is suggested. An example of numerical modeling for a natural gas liquefaction plant based on the modular constructions of the process line is provided.

Direct Numerical Modeling as a Tool for Optical Coherence Tomography Development: SNR (Sensitivity) and Lateral Resolution Test Target Interpretation

Optical Coherence Tomography (OCT) is a growing family of biophotonic imaging techniques, but in the literature there is a lack of easy-to-use tools to universally directly evaluate a device’s theoretical performance for a given metric. Modern computing tools mean that direct numerical modeling can, from first principles, simulate the performance metrics of a specific device directly without relying on analytical approximations and/or complexities. Here, we present two different direct numerical models, along with the example MATLAB code for the reader to adapt to their own systems. The first model is of photo-electron shot noise at the detector, the primary noise source for OCT. We use this firstly to evaluate the amount of additional noise present (1.5 dB) for an experimental setup. Secondly, we demonstrate how to use it to precisely quantify the expected shot noise SNR limit difference between time-domain and Fourier-domain OCT systems in a given hypothetical experiment. The second model is used to demonstrate how USAF 1951 test chart images should be interpreted for a given lateral PSF shape. Direct numerical modeling is an easy and powerful basic tool for researchers and developers, the wider use of which may improve the rigor of the OCT literature.

Tailings Behavior Assessment Using Piezocone Penetration Test

Intensive economic development is associated with an increasing demand for raw materials, including minerals. An illustrative example of this issue is the development of the copper industry. A significant problem arising from the scale of copper production is the management of an ever-growing amount of post-flotation tailings. This necessitates the need to ensure the continuity of safe storage. This study presents the results of studies on the behavior of deposits in the Żelazny Most Tailings Storage Facility (Poland). The primary objective of this study was to estimate the settlements of tailings under variable deposition conditions. The results were assessed using two methods: indirect and direct; this was based on cone penetration test (CPTU) results. The results were verified using Modified Cam Clay (MCC) modeling. Depending on the type of test, settlements ranged from several dozen centimeters to over three meters. Despite the observed differences, the results of both CPTU methods indicate a convergent trend in tailings behavior. Conversely, the results estimated using the direct method and numerical modeling demonstrate a high level of agreement.

Model of a Magnetoactive Elastomer with Structure Parameter

Purpose. To propose a simple and physically reasonable way to describe basic properties of magnetoactive elastomers under the action of magnetic field and/or mechanical loading.Methods. A phenomenological approach is developed, in the framework of which the aggregation of ferroparticles in a magnetoactive elastomer is interpreted as the appearance of an order parameter whose physical meaning resembles, although does not coincide entirely with, the number of the particles dwelling in aggregates normalized by the total number of the particles. The corresponding functional contribution to the free energy of the system is constructed in the form similar to that of the Landau-de Gennes expansion, as it is used in the theory of phase transitions. Depending on the presence of the cubic term in this expansion, the transition may develop along the scenarios of either I or II order.Results. In a model 1D calculation it is shown that the dependences of the main characteristics of the composite, viz. magnetization and deformation, on the applied field and mechanical load, might be in a unified manner described as being entailed by the evolution of the above-introduced order parameter. A specific feature manifested by the model system is its ability to display quasi-plastic response that exists as long as the external field is on, and to get back to elastic behavior as soon as the field is switched off.Conclusions. The results obtained are found to be in good agreement with the data obtained from the direct numerical modelling of the mesoscopic variant of the considered problem. In qualitative aspect, the discovered specific features of the rheological bahavior closely resemble the results of experimental studies om mechanical loading of magnetoactive composites consisting of a silicone rubber filled with micron-size particles of carbonyl iron.

О ЗАВИСИМОСТИ ТУРБУЛЕНТНОЙ ВЯЗКОСТИ ОТ ЧИСЛА РЕЙНОЛЬДСА ДЛЯ ТЕЧЕНИЙ В ТРУБАХ

The work shows that the ratio of turbulent viscosity to kinematic viscosity and the Reynolds number calculated from the dynamic velocity weakly depends on the Reynolds number, but this dependence is not monotonic. Data from direct numerical modeling of turbulent flow in pipes known from the literature show that if, instead of the Reynolds number calculated from the dynamic velocity, we use the Reynolds number calculated from the average velocity over the cross section, the indicated dependence becomes monotonic and at large values of the Reynolds number the ratio of turbulent viscosity to kinematic viscosity and Reynolds number tends to a finite limit. Formulas are obtained for calculating the maximum value of turbulent viscosity and the cross-sectional average value depending on the Reynolds number.

Исследование электровихревого течения между плоскостями с помощью различных вычислительных подходов

Electrovortex flows arise when an electric current of varying density passes through a well-conducting fluid (e.g., acid or metal melt). In such a case, the electric current generates a magnetic field, which leads to the Lorentz force causing swirling currents of the medium. There are different methods of theoretical study of such currents. As a rule, to avoid the necessity to find the pressure dependence on coordinates, the variables "vector potential of velocity - swirl" ("scalar current function – swirl" in the case of axisymmetric flows) are used. In such a case, it is quite effective to use automodel variables, which allow to reduce the dimensionality of the problem. In this case, the solution for the introduced function can be sought in the form of an expansion by the electro-vortex flow parameter proportional to the square of the magnetic Reynolds number. Also, this solution can be obtained numerically, for example, using finite-difference methods. Nowadays, more and more often the solutions are investigated by means of direct numerical modeling methods, when no automodel approximations are made, which reduce the accuracy of the solution. Nevertheless, in such a case the number of computations can be quite large and requires the use of supercomputer resources. A separate difficulty is presented by the boundary conditions: for example, for the velocity vector potential we obtain a fourth-order equation, which imposes significant restrictions on the time steps in the evolution equation. The problem can be avoided by using approximate boundary conditions, but this again reduces the accuracy of the solution. In this paper, using the example of electro-vortex flow between planes, the solutions that can be obtained using the various computational approaches mentioned above are examined. The results obtained are compared, and they are also compared with analytical approximations.

Utilization of 3-D Volume of Fluid Simulations to Understand Oxygen Evolution through Multilayer Porous Transport Layers for PEMWE Improvement

In this work, direct numerical modeling techniques were applied to 3-D generated porous transport layers (PTL), with the addition of a microporous layer (MPL), to understand the effect pore structure has on oxygen evolution. Proton Exchange Membrane Water Electrolyzers rely on PTLs to remove oxygen from the catalyst layer. Traditionally, an MPL is added to the PTL surface in contact with the catalyst layer. This creates a bilayer PTL, which is believed to improve oxygen removal, while maintaining liquid saturation. Two questions arise when creating a PTL sample for PEMWE application. First, how thick should the MPL be to achieve adequate oxygen removal? Second, is a bilayer PTL sufficient, or does a multilayer PTL result in improved oxygen removal?The objectives of this work are to observe the influence that the MPL has on oxygen transport, the effect of the MPL on oxygen removal when compared to a single layer PTL, determine an ideal MPL to PTL ratio, and identify if multilayer PTLs aid in oxygen removal. Each sample is created through an improved image processing technique that eliminates the need for interface communication when meshing. This process allows for multilayer PTL structures to be created as one geometry. Due to the improved imaging technique, meshing of these complex structures is possible. The Finite Volume Method combined with a volume of fluid model was used to simulate two phase flow, liquid water and gaseous oxygen, through all PTL samples. Each PTL/MPL combination has three different MPL thickness, which corresponds to a PTL/MPL ratio of 90:10, 80:20, and 70:30. Bilayer, trilayer, and quadlayer PTL samples were also studied. Oxygen bubble evolution, growth, and surface interaction through all sample microstructures was observed. In-plane and through-plane permeability, liquid saturation, and liquid/gas interfacial area were calculated from simulation results. Findings from this work will provide insight into ideal MPL thickness and number of MPL layers for improved oxygen removal inside PEMWEs.

Control of brine composition over reactive transport processes in calcium carbonate rock dissolution: Time-lapse imaging of evolving dissolution patterns

This study investigates the impact of brine composition—specifically calcium ions and NaCl-based salinity—on the development of dissolution features in Ketton, a porous calcium carbonate rock. Utilizing a laboratory XMT (X-ray microtomography) scanner, we captured time-lapse in situ images of Ketton samples throughout various dissolution experiments, conducting four distinct flow-through experiments with differing brine solutions at a flow rate of 0.26 ml min⁻1. The scans yielded a voxel size of 6 μm, enabling the assessment of the temporal evolution of porosity and pore structure through image analysis and permeability evaluations via single-phase fluid flow simulations employing direct numerical solutions and network modeling, as opposed to direct measurement.Time-lapse imaging technique has delineated the extent to which the concentrations of CaCl₂ and NaCl in the injecting solution control the structural evolution of dissolution patterns, subsequently triggering the development of characteristic dissolution pattern. The inflow solution with no Ca2+ ions and with the minimal salt content manifested maximum dissolution near the sample inlet, coupled with the formation of numerous dissolution channels, i.e., wormholes. Conversely, solutions with a trace amount of Ca2⁺ ions induced focused dissolution, resulting in the formation of sparsely located channels. Inflow solutions with high concentrations of both Ca2⁺ ions and salt facilitated uniformly dispersed dissolution, primarily within microporous domains, initiating particle detachment and displacement and leading to localized pore-clogging. The relative increase in permeability, in each experiment, was correlated with the developed dissolution pattern. It was discerned that varying ratios of salt and calcium concentrations in the injected solution systematically influenced image-based permeability simulations and porosity, allowing for the depiction of an empirical porosity-permeability relationship.

Thermal structure beneath Changbaishan Volcano, northeastern Asia: new insights from temperature logging and numerical modelling

SUMMARY Changbaishan Volcano is considered one of the most hazardous active volcanic fields in northeastern Asia, and it has been the subject of increasing concern due to its unrest from 2002 to 2006. The physical conditions of magma chambers in the crust, particularly temperature and pressure, are crucial factors that determine the tempo and magnitude of volcanic eruptions, which are closely linked to potential hazards. However, the lithospheric thermal structure, which strongly influences rheological behaviour and melting, has been poorly studied. We conducted direct geothermal measurements and numerical forward modelling to address this issue to confirm whether a crustal magma chamber lies beneath the caldera as in earlier geophysical interpretations. We first reported four heat-flow data sets in Changbaishan Volcano. The research findings indicate that the heat flow value near the Tianchi caldera is remarkably high, at 270±16 mW m−2. As the distance from the caldera increases, the heat flow gradually decreases to a normal continental heat flow value of 75 mW m−2. 3-D transient heat simulations with a magma cooling model and a continuous magma supply model demonstrate the thermal effect of the magma chamber. The best-fitting model for the Tianchi magma system is an ellipsoidal magma chamber with a depth of 8–14 km, a 20 km east–west axis and a 70 km north–south axis, supplied with magma from the asthenosphere for 2 Myr. The high surface heat flow and crustal temperatures suggest that magma is active beneath Changbaishan Volcano within the middle-upper crust, and volcanic reactivation could occur. Thus, further research on the lithospheric thermal structure is necessary to understand the potential volcanic hazards associated with Changbaishan Volcano.

Investigating the Slope Stability and Factor of Safety Properties of Soil Reinforced with Natural Jute Fibers under Different Rainfall Conditions

Heavy rainfall is often responsible for embankment failures. During intense rainfall, the embankment slope inclination is vital for slope stability. Some failures occur in the slope due to heavy rainfall and sudden change in the matric suction. Jute fiber is a reinforcing material that is added to improve soil strength. In this research, in order to explore the effects of slope inclination on soil stability, soil samples were collected and exposed to artificial rainfalls. This study presented various tests performed on the soil samples. Different tests like sieve analysis, permeability test, Direct Shear Test (DST), liquid limit, plasticity limit, and numerical modeling were conducted in the laboratory. The study's findings revealed that the failure is caused by a soil suction loss when the inclination of the slope is higher than the soil friction angle and the collapse is caused by the positive water pressure at the slope's toe when it is lower than the soil's friction angle. Furthermore, when the slope angle increases, the slopes are becoming increasingly vulnerable to rapid collapse. After that, jute fibers were combined with the soil to improve its performance. Samples of 2, 3, and 4 rows of jute fibers were tested. These jute fiber samples performed better than the ones without fibers under different rainfall conditions. The distribution of jute fibers had a favorable influence on both strength measurements and safety aspects. Utilizing the factor of safety and matric suction, the performance of jute fiber samples is superior to those without jute fibers. Consequently, by adding jute fibers the stabilization of the soil is significantly improved along with its factor of safety.

A novel boundary tracing method without enrichment for modeling cracks and their propagation

A novel direct numerical modeling method for preexisting cracks and their propagation is developed based on the integral-generalized finite difference (IGFD) method which has an excellent performance in accuracy, flexibility, and convenience in dealing with boundary conditions. “Direct modeling” means discontinuities and their propagation are directly treated as boundaries of subdomains. The standard IGFD method for continuity problems is adopted in regions far from discontinuities, while modifications are required around the discontinuities. Some special treatments such as paired nodes and birth–death algorithms are employed to characterize the existing cracks and track the crack growth path. These techniques together constitute the extended IGFD (xIGFD) method realizing the application of IGFD method in discontinuity problems. Three specific technologies, xIGFD-A, xIGFD-B, and xIGFD-C are proposed to treat the growing nodes along the discontinuities. The xIGFD-A needs to number the newly generated nodes and add degrees of freedom for propagating cracks, which would change the dimensions of the global matrices, while the xIGFD-B and the xIGFD-C do not. The successful applications of this proposed xIGFD method as well as the comparisons with existing numerical methods in a series of examples involving quasi-static propagation of a single crack and cross cracks have fully proved its effectiveness and superiority. The proposed method neither needs enriched basis functions based on prior knowledge nor requires re-meshing operations, which shows the unity and conciseness of the discretization scheme for continuity and discontinuity problems. Therefore, it has application potential in more complex practical problems like hydraulic fracturing and fatigue cracks.

Seawater signatures of Ordovician climate and environment

Abstract Tracking climatic changes throughout the Ordovician is crucial to a better understanding of the coevolution of life and environment on Earth. Ordovician climate fluctuations have been the subject of a vigorous and productive body of work over the past two decades. Here we present a synthesis of studies that have focused on reconstructing Ordovician climate and environment via direct geochemical proxy datasets and/or numerical modelling approaches. Many new insights have been gained on potential causes of events: the timing and potential causes of the major radiation of Ordovician marine life, changes in weathering and the transition from a greenhouse-to-icehouse state, and cooling and (de)oxygenation during the end-Ordovician Glaciation. Marked improvements in sample resolution/distribution of traditional palaeotemperature (oxygen isotopes), palaeoredox (sulfur isotopes) and weathering proxy records (strontium and neodymium isotopes), as well as the development of new palaeoenvironmental proxies (e.g. clumped, uranium, molybdenum and thallium isotopes; iodine, iron, trace metal geochemistry), have led to better constraints on Ordovician climate and environment. These recent works have led to a more nuanced understanding of the Ordovician Earth System, which allows the global community to focus future efforts on answering remaining questions regarding palaeoclimate and environment, as well as embark upon new investigations.

О вибрационной неустойчивости Кельвина-Гельмгольца для жидкостей сравнимых вязкостей

We study the behavior of a two-dimensional system of immiscible incompressible viscous liquids in a rectangular cavity under horizontal harmonic high-frequency vibrations. In this system, influ-ence of pulsating motions of the liquids causes the development of Kelvin-Helmholtz instability leading to the formation of a quasi-stationary relief on the interfacial surface in the form of a frozen wave. A direct numerical modeling of the relief formation was carried out with the use of AN-SYS Fluent software; the influence of the viscosity ratio on the parameters of the frozen wave and the flow generated by vibrations near the interface was investigated. The dependencies of the char-acteristics of the wave relief on supercriticality and vibration frequency are plotted for different ra-tios of liquid viscosities. In the cases of vibrations with sufficiently high frequency, the obtained numerical results are consistent with analytical theory developed for ideal liquids. For lower fre-quencies, the observed relief wavelength turns out to be noticeably longer than the theoretical pre-dictions. For high vibration frequencies, with increasing supercriticality the wavelength increases monotonically, while for low frequencies it decreases monotonically. The relief height increases as the intensity of vibration influence increases; with significant supercriticality, it exceeds the theo-retical values obtained in the ideal fluid approximation. The generation of reverse averaged flow by vibrations near the interface is found when viscosity of the upper fluid is low. In this case, the flows in the upper and lower liquids are directed opposite to each other and a noticeable decrease in the average flow generation intensity is observed.

Nonlinear waves of the sine-Gordon equation in the model with three attracting impurities

Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of coupled localized nonlinear waves in the sine-Gordon model with impurities (or spatial inhomogeneity of the periodic potential). Methods. Using the analytical method of collective coordinates for the case of the arbitrary number the same point impurities on the same distance each other, differential equation system was got for localized waves amplitudes as the functions on time. We used the finite difference method with explicit scheme for the numerical solution of the modified sine-Gordon equation. We used a discrete Fourier transform to perform a frequency analysis of the oscillations of localized waves calculate numerically. Results. We found of the differential equation system for three harmonic oscillators with the elastic connection for describe related oscillations of nonlinear waves localized on the three same impurity. The solutions obtained from this system of equations for the frequencies of related oscillation well approximate the results of direct numerical modeling of a nonlinear system. Conclusion. In the article shows that the related oscillation of nonlinear waves localized on three identical impurities located at the same distance from each other represent the sum of three harmonic oscillations: in-phase, in-phase-antiphase and antiphase type. The analysis of the influence of system parameters and initial conditions on the frequency and type of associated oscillations is carried out.

Comparing Direct Numerical Modeling Predictions With Field Evidence for Methane Vertical Microseepage in Two Geological Settings

The footprints of petroleum microseepage can be associated with chemical and microbial processes in initially homogeneous strata and/or with the fluid transport properties of the rocks through which oil and gas migrate. This work examines the role of such driving factors in two contrasting geological settings by comparing numerical modeling predictions for upward methane microseepage with some field evidence for hydrocarbons transport and accumulation. The two case studies are a monitoring borehole (BH8) from a landfill in southern Ontario, Canada, and an oil well (Saltarin 1A) from the Eastern Llanos Basin in Colombia. Profiles of relative methane concentrations versus depth were generated using a time-dependent, one-dimensional, simulation of the advection-diffusion equation applied to multiple strata of soils, and sediments. The model employs the layered sequences of these two geological settings. The results obtained hinge on the standard permeability values for the rock types involved and their corresponding flow velocities and diffusion coefficients. Resistivity logs were utilized as direct proxies of hydrocarbon concentrations. As additional evidence for petroleum microseepage, experiments of electron paramagnetic resonance (EPR) were carried out in drilling cuts of Saltarin 1A to measure traces of organic matter free radicals concentrations (OMFRC). Extractable organic matter (EOM) and magnetic susceptibility data were also considered in interpreting the EPR results. Qualitative comparisons between modeled methane profiles and their corresponding resistivity logs suggest that microseepage and hydrocarbon accumulations are conditioned by the fluid transport properties of the rocks contained by BH8 and Saltarin 1A. Moreover, in most of the Saltarin 1A sequence, the OMFRC profiles follow the trends displayed by the resistivity and modeled methane logs. Thus, the EPR data also indicates that hydrocarbon microseepage and accumulation are largely controlled by lithology. Conversely, EOM and magnetic susceptibility appear to be evidence for hydrocarbon-mediated near-surface chemical processes.

Numerical modeling for 3D vortices patterns of electroconvective flow developing in shear flow

In this study, using direct numerical modeling, we investigate the electroconvective flow developing on the surface of an ion-exchange membrane surface in the high applied voltage condition. The modeling is obtained by solving the system of Poisson–Nernst–Planck–Navier–Stokes equations in a direct and coupled manner on the OpenFOAM platform. We report simulation results proving the dependence of the flow's pattern on the applied voltage and the mechanism behind the formation of vortices at high electric fields. For the first time, different types of vortices and the concurrent appearance of helical and unidirectional vortices are studied. The role of the vortices on the distribution of ions and the electric current is clarified to explain the over-limiting current phenomenon. This work contributes a useful OpenFOAM solver integration tool for modeling electrochemical problems.

Scattering of an Ostrovsky wave packet in a delaminated waveguide

We examine the scattering of an Ostrovsky wave packet, generated from a solitary wave, in a two layered waveguide with a delamination in the centre and soft (imperfect) bonding either side of the centre. The lower layer of the waveguide is assumed to be significantly denser than the upper layer, leading to a system of Boussinesq–Klein–Gordon (BKG) equations. Direct numerical modelling is difficult and so a semi-analytical approach consisting of several matched asymptotic multiple-scale expansions is used, which leads to Ostrovsky equations in soft bonded regions and Korteweg–de Vries equations in the delaminated region. The semi-analytical approach and direct numerical simulations are in good agreement with each other and theoretical estimates. The dispersion relations are used to estimate the wave speed and hence classify the length of the delamination, in addition to changes in the amplitude of the wave packet. We also show how to scale the non-dimensional results to material variables and an example for PMMA is presented. These results can provide a tool to control the integrity of layered structures.

Computational Approach for the Fluid-Structure Interaction Design of Insect-Inspired Micro Flapping Wings

A flight device for insect-inspired flapping wing nano air vehicles (FWNAVs), which consists of the micro wings, the actuator, and the transmission, can use the fluid-structure interaction (FSI) to create the characteristic motions of the flapping wings. This design will be essential for further miniaturization of FWNAVs, since it will reduce the mechanical and electrical complexities of the flight device. Computational approaches will be necessary for this biomimetic concept because of the complexity of the FSI. Hence, in this study, a computational approach for the FSI design of insect-inspired micro flapping wings is proposed. This approach consists of a direct numerical modeling of the strongly coupled FSI, the dynamic similarity framework, and the design window (DW) search. The present numerical examples demonstrated that the dynamic similarity framework works well to make different two FSI systems with the strong coupling dynamically similar to each other, and this framework works as the guideline for the systematic investigation of the effect of characteristic parameters on the FSI system. Finally, an insect-inspired micro flapping wing with the 2.5-dimensional structure was designed using the proposed approach such that it can create the lift sufficient to support the weight of small insects. The existing area of satisfactory design solutions or the DW increases the fabricability of this wing using micromachining techniques based on the photolithography in the micro-electro-mechanical systems (MEMS) technology. Hence, the proposed approach will contribute to the further miniaturization of FWNAVs.

Оптические свойства кремниевых нанопилларов со встроенным вертикальным p-n-переходом

Resonance reflection of light from the ordered arrays of silicon nanopillars (Si NP) was investigated. The height of Si NP was 450 nm. The effect of Si NP oxidation in concentrated nitric acid on the position of resonances in reflection spectra was studied. A weak influence of the additional polymeric coating on the characteristics of reflection from the structures was proven. It is established on the basis of the results of experimental investigation and direct numerical modeling by means of three-dimensional finite difference time domain algorithm (3D FDTD) that the dependence of the resonant wavelength for Si NP on the diameter of Si NP is a linear function with nonzero displacement depending on the pitch.