Equations Of Motion For Particles Research Articles

ПОВЫШЕНИЕ ЭНЕРГЕТИЧЕСКОЙ И ЭКОЛОГИЧЕСКОЙ ЭФФЕКТИВНОСТИ СИСТЕМ ГАЗООЧИСТКИ НА ТЭС

Актуальность исследования обусловлена необходимостью повышения энергетической и экологической эффективности систем очистки выбросов систем пылеприготовления и дымовых газов ТЭС при угольной генерации и систем подготовки газа при газовой генерации, во исполнение Федерального закона № 261-ФЗ от 23.11.2009 г. (ред. от 29.07.2017) «Об энергосбережении и о повышении энергетической эффективности и о внесении изменений в отдельные законодательные акты Российской Федерации», а также требований по контролю за выбросом парниковых газов (напр., приказа № 330 от 29.06.2017 года «Об утверждении методических указаний по количественному определению объёма косвенных энергетических выбросов парниковых газов» и др.) выбросов систем пылеприготовления и дымовых газов ТЭС с угольной генерацией и в системе подготовки газа с газовой генерацией. Цель: разработка устройства циклонной фильтрации для повышения эффективности систем газоочистки на ТЭС, снижения выбросов взвешенных частиц в атмосферу от систем пылеприготовления и дымовых газов при угольной генерации и увеличения надежности работы агрегатов газотурбинных и парогазовых установок ТЭС вследствие снижения износа рабочих поверхностей поршневых и винтовых дожимающих компрессоров дожимных компрессорных станций, предотвращения попадания продуктов внутренней коррозии газопроводов в газотурбинных установках, в соответствии с п.п. 93, 94 ФНиП в области промышленной безопасности «Правила безопасности сетей газораспределения и газопотребления» (Серия 12, вып. 13). Объект: модель циклона на базе ЦН-11-200, обеспечивающая повышение энергетической и экологической эффективности систем газоочистки на ТЭС. Методы: стендовые испытания циклонного фильтра, изготовленного путем модернизации циклона ЦН-11-200, аэродинамические расчёты; численное моделирование аэродинамических параметров работы циклона-фильтра на основе методов вычислительной гидродинамики. Для математического моделирования процесса сепарации использована система уравнений, состоящая из осредненных по Рейнольдсу уравнений движения однофазного потока Навье–Стокса и уравнения движения частиц, основанного на законе Ньютона. Для определения эффективности отделения взвешенной части потока в циклоне-фильтре использован безразмерный комплекс Rer, с помощью которого численные значения параметров осаждения взвеси из многофазного потока в сепараторе найдены расчетным путем. Результаты. Анализ литературных источников показал отсутствие конструкций циклонов-фильтров, которые обеспечивали бы надлежащую (более 98 %) степень очистки выбросов без резкого увеличения энергозатрат на обработку выбросов. Проведенные опыты показали целесообразность конструктивного дополнения возвратно-поточных циклонов фильтрующей вставкой в зоне, где происходит инерционное осаждение пыли. Для определения эффективности отделения взвешенной части потока в данном циклоне-фильтре был использован безразмерный комплекс Rer. Расчеты показали соответствие результатов теоретических и натурных исследований.

Embolus Transport Simulations with Fully Resolved Particle Surfaces.

There has been interest in recent work in using computational fluid dynamics with Lagrangian analysis to calculate the trajectory of emboli-like particles in the vasculature. While previous studies have provided an understanding of the hemodynamic factors determining the fates of such particles and their relationship to risk of stroke, most analyses have relied on a particle equation of motion that assumes the particle is "small" e.g., much less than the diameter of the vessel. This work quantifies the limit when a particle can no longer be considered "small". The motion of embolus-like particles are simulated using an overset mesh technique. This allows the fluid stresses on the particle surface to be fully resolved. Consequently, the particles can be of arbitrary size or shape. The trajectory of resolved particles and "small" particles are simulated through a patient-specific carotid artery bifurcation model with particles 500, 1000, and 2000μm in diameter. The proportions of particles entering the internal carotid artery are treated as the outcome of the particle fate, and statistical comparisons are made to ascertain the importance of non-small particle effects. For the 2000μm embolus, the proportion of particles traveling to the internal carotid artery is 74.7 ± 1.3% (mean±95% confidence margin) for the "small" particle model and is 85.7±5.4% for a resolved particle model. The difference is statistically significant, [Formula: see text], based on the binomial test for the particle outcomes. No statistically discernible differences are found for the smaller diameter particles. Quantitative differences are observable for the 2000μm trajectories between the "small" and resolved particle models which is a particle diameter 27% relative to the common carotid artery diameter. A fully resolved particle model ought to be considered for emboli trajectory simulations when the particle size ratio is ≳20%.

Mapping of power deposition zone of electron Bernstein waves externally excited in tokamak plasmas

In toroidal plasmas, electron Bernstein (EB) waves mode-converted from X waves at the upper hybrid resonance (UHR) layer propagate toward the higher field side and are cyclotron-damped away at Doppler shifted frequency before arriving at the electron cyclotron resonance (ECR) layer. Resulting power deposition profile depends on local density, temperature and field profiles and is usually analyzed using the ray tracing technique for EB wave propagation and absorption in inhomogeneous magnetized plasmas. In axisymmetric tokamak plasmas, the ray tracing equation of EB waves can be cast into the form of equation of particle motion in a potential field. The particle trajectory and its momentum correspond to the wave trajectory and the refractive index, respectively. The potential field reflects the dispersion characteristics of EB waves, that is, the perpendicular refractive index strongly increases as the waves approach to the ECR layer from the lower field side, making a deep trench of potential along the ECR layer. Therefore the EB waves perpendicularly approach the ECR layer, which enable us to estimate the parallel refractive index and the parallel velocity of resonance electrons near the ECR layer. Thus, possible power deposition zone can be mapped and the associated current drive efficiency is roughly estimated directly from the information on wave frequency and plasma profiles without ray tracing calculations (direct mapping). The mapped zone, in the case of a moderately over dense plasma, is shown to be coincident with the ray tracing results for both XB and OXB schemes of mode conversion. In the cases of highly over dense, low safety factor and low aspect ratio plasmas, ω/Ωce is rather close to two at the UHR layer and the second harmonic cyclotron damping can take place along the ray trajectory just after OXB mode conversion, depending on the parameters. Here, ω is the wave frequency and Ωce is the local cyclotron frequency. It is shown that direct mapping also works in this case as well. The direct mapping technique is based on above picture of EB wave propagation and absorption, and is useful to guide the ray tracing analyses and cross-check the ray tracing results.

A fictitious domain method for particulate flows of arbitrary density ratio

In this paper, our previous direct-forcing fictitious domain method is modified for particle-laden flows of arbitrary density ratio. The instability of original scheme for low density ratio is circumvented by a simple modification in the particle motion equations, with the key idea of increasing the coefficient of particle inertial term. Three schemes are proposed, which are shown to be equally accurate. The modified DF/FD method is extensively validated with various tests, and it is shown that the accuracy of our method is comparable to previous methods. In addition, our method is applied to the direct numerical simulations of the motion of finite-size particles (or bubbles) in a vertical turbulent channel flow of the density ratio 0.001. Our results indicate that the effects of particle-fluid density ratio on turbulent channel flow are negligibly small when the density ratio is smaller than unity and the gravity effect is not considered. The fluid Reynolds shear stress and the wall friction are enhanced in upflow where the particles are aggregated near the wall, whereas they are reduced in downflow where the particles move towards the channel center.

Alteration of Particle Drift Resonance Dynamics Near Poloidal Mode Field Line Resonance Structures

AbstractWe examine the effect on drift‐resonant particle dynamics of a strongly peaked internally driven poloidal mode field line resonance (FLR; with specified frequency ω in the Pc5 range and azimuthal mode number m≫1). Using an analytic magneto‐hydrodynamic model in a dipole field to describe the ultra low frequency wave mode, we use the bounce‐averaged formalism of Northrop (1963) to obtain equations of motion for charged particles in the wave frame and find an analytic solution for the case of a temporally constant ultra low frequency wave amplitude profile. Focusing on equatorially mirroring electrons in this study, we demonstrate that, for sufficiently peaked radial profiles, multiple drift resonances appear that are associated with the FLR peak. These are in addition to the well‐known zeroth‐order drift resonance location, occurring when the unperturbed drift speed satisfies the resonance condition ( ). The additional resonances arise because the strongly peaked FLR wave field components provide sufficiently strong perturbations to the azimuthal drift speed to cause multiple zero crossings in the resonance condition. These additional resonances have trapping periods much lower than that of the zeroth‐order resonance and considerably complicate the electron dynamics. Further properties of these resonances and their measurable effect on electron dynamics are discussed. For example, their effect on observations of energetic electron flux on board satellites in the vicinity of an FLR is calculated and shown to significantly distort the typical signature associated with drift resonance (modulations in electron flux at the wave frequency with a 180° phase change across the resonant energy).

Experimental and numerical studies of the gas-molten reduction behavior of blast furnace dust particles during in-flight process

Blast furnace (BF) dust is a typical solid waste produced in manufacturing iron, which can be recycled effectively through in-flight reduction technology. In this work, the gas-molten reduction behavior of BF dust particles during in-flight process was analyzed experimentally and mathematically. The experimental results shown that the effects of temperature and gas composition on the reduction degree were significant. The morphological observation found that the dust particle was completely melted down at 1723 K and the generated metallic iron was entrapped and aggregated into a perfect sphere in the molten particle. The kinetic analysis revealed that the reduction process is controlled by the chemical reaction at the gas-molten interface and the activation energy was determined to be 246 kJ/mol. A computational fluid dynamics (CFD) model was also developed to study the fluid flow, heat transfer and chemical reactions involved in the reduction process, where the reduction gas was treated as a continuum and the dust particles were tracked by Lagrangian approach. A recirculation zone and a low gas temperature region were predicted near the top part region of the reactor. The accurate particle residence time was calculated by solving particle motion equations with the introduction of particle relaxation time. Non-isothermal particle temperature profiles inside the reactor were obtained, and were taken into consideration for the chemical reactions. The simulated terminal reduction degrees agree well with the experimental results.

Analytic solutions of the geodesic equation for Reissner-Nordström–(anti–)de Sitter black holes surrounded by different kinds of regular and exotic matter fields

The purpose of this study is the derivation of the equation of motion for particles and light in the spacetime of Reissner-Nordstr\"{o}m-(anti-)de Sitter black holes in the background of different kinds of regular and exotic matter fields. The complete analytical solutions of the geodesic equations are given in terms of the elliptic Weierstra{\ss} $\wp$-function and the hyperelliptic Kleinian $\sigma$-function. Finally after analyzing the geodesic motion of test particles and light using parametric diagrams and effective potentials, we present a list of all possible orbits.

Numerical simulation of the impact of laying powder on selective laser melting single-pass formation

Selective laser melting (SLM) is an additive manufacturing technology to directly form complex metal parts. It has been demonstrated in aerospace and other fields. In the SLM single-pass formation process, the SLM layer distribution was modeled here via the discrete element method model (particle contact force model and particle motion equation). A dynamic behavior model of molten pool based on the particle scale was also established. The governing equations considered the influence of thermodynamic factors such as Marangoni effect, gasification recoil, and gasification heat dissipation. The laser energy model used a Gaussian heat source based on interface tracking. To study the influence of laying powder on SLM single-pass formation, the corresponding simulations were performed from three aspects: particle size distribution, powder bed tightness, and lamination thickness. To obtain a good formation zone in the actual SLM process, metal powder with a smaller average particle size should be used on the basis of saving money, and the proportion of large-sized particles in the powder should be minimized. A higher powder bed tightness is needed on the basis of ensuring a good connection with the substrate or the previous printed layer. Finally, a larger lamination thickness should be used on the basis of ensuring that the powder bed is sufficiently melted in the formation zone. This paper is expected to provide some guidance for the actual SLM laying powder process.

The equatorial motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime

In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We investigate the conditions for existence of bound orbits in causality-preserving region as well as the conditions for existence of circular orbits for charged and uncharged particles. We also study the effect of NUT parameter on Newtonian orbits. Finally, we give exact analytical solutions of equations of equatorial motion for a charged test particle.

Improving Energy and Environmental Efficiency of Flue Gas Cleaning at Thermal Power Plants

The aim of the work is to improve cyclone and filter dust collectors by increasing the efficiency of fine particle deposition classes PM10, PM2,5 as well as reducing energy and material costs. The analysis of existing methods of cyclonic filtration of industrial dispersed emissions is carried out. The laboratory tests of the cyclone filter, made by modernization of the cyclone CN-11-200, were performed, the aerodynamic characteristics of its operation were found. The calculated determination of the efficiency of suspension deposition from multiphase flow in the separator using a dimensionless Rer criterion is performed, derived from the Navier-Stokes single-phase flow equations of motion and the particle motion equation based on Newton’s law. A numerically studied the aerodynamic parameters of the cyclone on the basis of computational fluid dynamics methods. For mathematical modeling of turbulence we used the DES model

Dynamics of Love-Type Waves in Orthotropic Layer Under the Influence of Heterogeneity and Corrugation

The present problem deals with the propagation of Love-type surface waves in a bedded structure comprises of an inhomogeneous orthotropic layer and an elastic half-space. The upper boundary and the interface between two media are considered to be corrugated. An analytical method (separation of variables) is adapted to solve the second order PDEs, which governs the equations of motion. Equations for particle motion in the layer and half-space have been formulated and solved separately. Finally, the frequency relation has been established under suitable boundary conditions at the interface of the orthotropic layer and the elastic half-space. Obtained relation is found to be in good agreement with the classical case of Love wave propagation. Remarkable effects of heterogeneity and corrugation parameters on the phase velocity of the considered wave have been represented by the means of graphs. Moreover, the group velocity curves are also plotted to exhibit the profound effect of heterogeneity considered in the layer. Results may be useful in theoretical study of wave propagation through composite layered structure with irregular boundaries.

The approximate solution of charged particle motion equations in oscillating magnetic fields using the local multiquadrics collocation method

The charged particle motion for certain configurations of oscillating magnetic fields can be simulated by a Volterra integro-differential equation of the second order with time-periodic coefficients. This paper investigates a simple and accurate scheme for computationally solving these types of integro-differential equations. To start the method, we first reduce the integro-differential equations to equivalent Volterra integral equations of the second kind. Subsequently, the solution of the mentioned Volterra integral equations is estimated by the collocation method based on the local multiquadrics formulated on scattered points. We also expand the proposed method to solve fractional integro-differential equations including non-integer order derivatives. Since the offered method does not need any mesh generations on the solution domain, it can be recognized as a meshless method. To demonstrate the reliability and efficiency of the new technique, several illustrative examples are given. Moreover, the numerical results confirm that the method developed in the current paper in comparison with the method based on the globally supported multiquadrics has much lesser volume computing.

Classical neutral point particle in linearly polarized EM plane wave field

We study a covariant classical model of neutral point particles with magnetic moment interacting with external electromagnetic fields. Classical dynamical equations which reproduce a correct behavior in the non-relativistic limit are introduced. We also discuss the non-uniqueness of the covariant torque equation. The focus of this work is on Dirac neutrino beam control. We present a full analytical solution of the dynamical equations for a neutral point particle motion in the presence of an external linearly polarized EM plane wave (laser) fields. Neutrino beam control using extremely intense laser fields could possibly demonstrate Dirac nature of the neutrino. However, for linearly polarized ideal laser waves we show cancellation of all leading beam control effects.

Palatini f(R,Lm,RμνTμν) gravity and its Born-Infeld semblance

We investigate Palatini $f(\mathcal{R},\mathcal{L}_m, \mathcal{R}_{\mu\nu}T^{\mu\nu})$ modified theories of gravity wherein the metric and affine connection are treated as independent dynamical fields and the gravitational Lagrangian is made a function of the Ricci scalar $\mathcal{R}$, the matter Lagrangian density $\mathcal{L}_m,$ and a "matter-curvature scalar" $\mathcal{R}_{\mu\nu}T^{\mu\nu}$. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum dependent metric, related to the physical metric by a matrix transformation. Similar to metric $f(\mathcal{R}, T, \mathcal{R}_{\mu\nu}T^{\mu\nu})$ gravity, the field equations impose the non-conservation of the energy-momentum tensor, leading to an appearance of an extra force on massive test particles. We obtain the explicit form of the field equations for massive test particles in the case of a perfect fluid, and an expression for the extra force. The nontrivial modifications to scalar fields and both linear and nonlinear electrodynamics are also considered. Finally, we detail the conditions under which the present theory is equivalent to the Eddington-inspired Born-Infeld (EiBI) model.

In Vitro Study of Particle Transport in Successively Bifurcating Vessels.

To reach a predictive understanding of how particles travel through bifurcating vessels is of paramount importance in many biomedical settings, including embolization, thromboembolism, and drug delivery. Here we utilize an in vitro model in which solid particles are injected through a rigid vessel that symmetrically bifurcates in successive branching generations. The geometric proportion and fluid dynamics parameters are relevant to the liver embolization. The volumetric flow field is reconstructed via phase-contrast magnetic resonance imaging, from which the particle trajectories are calculated for a range of size and density using the particle equation of motion. The method is validated by directly tracking the injected particles via optical imaging. The results indicate that, opposite to the common assumption, the particles distribution is fundamentally different from the volumetric flow partition. In fact, the amount of delivered particles vary substantially between adjacent branches even when the flow is uniformly distributed. This is not due to the inertia of the particles, nor to gravity. The particle distribution is rather rooted in their different pathways, which in turn are linked to their release origin along the main vessel cross-section. Therefore, the tree geometry and the associated flow streamlines are the prime determinant of the particle fate, while local changes of volumetric flow rate to selected branches do not generally produce proportional changes of particle delivery.

Multiphase partitions of lattice random walks

Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two lattice phases. In this letter we show that the hyperbolic hydrodynamic model obtained by enforcing the boundedness of lattice velocities derived in Giona M., Phys. Scr., 93 (2018) 095201 correctly describes the dynamics of the system and permits to derive easily the boundary condition at the interface, which, contrarily to the common belief, involves the lattice velocities in the two phases and not the phase diffusivities. The dispersion properties of independent particles moving on an infinite lattice composed by the periodic repetition of a multiphase unit cell are investigated. It is shown that the hyperbolic transport theory correctly predicts the effective diffusion coefficient over all the range of parameter values, while the corresponding continuous parabolic models deriving from Langevin equations for particle motion fail. The failure of parabolic transport models is shown via a simple numerical experiment.

Numerical modeling of particle motion and deposition in turbulent wavy channel flows

This work investigates the turbulent flow and particles deposition in wavy duct flows. The v2f turbulence model was used for simulating the turbulent flow through the wavy channel. The instantaneous turbulence fluctuating velocities were simulated using the Kraichnan Gaussian random field model. For tracking particles in the fluid flow, the particle equation of motion was solved numerically. The drag, Saffman lift, Brownian, and gravity forces acting on a suspended particle were included in the particle equation of motion. The effects of duct wave amplitude and wave length on deposition of particles of different sizes were studied. A range of waves with different amplitudes and wave lengths were simulated. The particle tracking approach was validated for turbulent flow in a flat horizontal channel where good agreement with previous studies was found. The presented results showed that the duct wavy walls significantly increase the particle deposition rate.

Modified Vlasov Equation and Collective Oscillations of Relativistic Radiating Electron Plasma

A Covariant Statistical Mechanics is developed for a system of electrons within the limits of plasma physics. By using the Landau-Lifshitz equation of motion for point charged particles, the phase space reduces to be a seven dimensional space instead of the ten dimensional space proposed by Hakim and Mangeney [J. Math. Phys. 1968, 9, 1, 116]. A modified Vlasov equation is obtained which permits one to deduce a general expression for the dispersion relations. Unlike other works, neither the Special Relativity nor any of the properties of the gauge are used to discard some of the wave modes. Instead, the continuity equation is used as a constraint embedded in the definition of the 4—vector current. This permits to make a mathematical analysis for calculating and discarding the transverse and longitudinal modes for any temperature. An expression for the longitudinal wave modes is deduced for any temperature and wave number. Usually, certain approximations are made to obtain such an expression that matches our result. But in general, without making such approximations, the result differs by a factor. The Landau damping and the damping due to the radiation reaction force are obtained and contrasted at low and high temperature cases. The results are compared with the ones obtained within Magnetohydrodynamics. Moreover, a numerical method is applied in order to compare the dispersion relations obtained with the approximations made. Surprisingly, it is sampled numerically that the dispersion relations are bounded for each temperature and that there is a cut-off for each wave number.

Suspended particle motion close to the surface of rotating cylindrical filtering membrane

The rotational filtration principle is known as an effective approach to slow the plugging of pores in a cylindrical filtering membrane. The existing applications are based on the study of the Taylor-Couette cell with a weak imposed radial inflow through a rotating inner cylinder. They are mostly related to thin filtration with a high transmembrane pressure. We consider a possible flow mode characterized by a high through-flow rate providing the subcritical liquid rotation within the inner cylinder boundary layer. An interphase interaction model is substantiated for the typical conditions considered and equations of a suspended solid particle motion are obtained in a dimensionless form giving similarity criteria of the problem. A number of benefits can be achieved with using this proposed flow mode when the particle size is one order of magnitude less than the boundary layer thickness. The influence of centrifugal force on the phase slip is the most notable when the particles are of the above size. It is possible, in particular, to exclude the contact of such particles with the membrane surface. The results obtained allow extending the application area of the high performance rotational filtration.

A fast and accurate numerical implementation of the envelope model for laser–plasma dynamics

In laser-driven, plasma wakefield acceleration regimes (LWFA), when relevant scale lengths of the laser envelope and of the driven plasma waves are well separated from the wavelength and frequency of the laser fast oscillating component, a reduced physical model (usually referred to as the envelope model), has been introduced, allowing to formulate the laser–plasma equations in terms of laser cycle-averaged dynamical variables. As a main consequence, physical regimes where this reduced model applies, can be investigated with significant savings of computational resources still assuring comparable accuracy, with respect to standard Particle-In-Cell (PIC) models where all relevant space–time scales have to be resolved.Here we propose a computational framework characterized by two previously unexplored numerical implementations of the envelope model. The first one is based on explicit second order leapfrog integration of the exact wave equation for laser pulse propagation in a laboratory coordinate system in 3D cartesian geometry, replacing the usually quoted representation in an Eulerian frame moving at the speed of light. Since the laser and driven wakefield wave equations in a laboratory frame are advection dominated, we introduce a proper modification of finite differences approximating longitudinal space derivatives, to minimize dispersive numerical errors coming from the discretized advection operators. The proposed implementation, avoiding semi-implicit procedures otherwise required when dealing with a comoving frame, assures significant saving in computational time and ease of implementation for parallel platforms. The associated equation of motion for plasma particles has been integrated, as in standard PIC codes, using the Boris pusher, properly extended to take into account the specific form of the Lorentz force in the envelope model.As a second contribution, a novel numerical implementation of the plasma dynamics equations in the cold-fluid approximation, is presented. The scheme is based on the second-order one-step Adams–Bashforth time integrator coupled to upwind non-oscillatory WENO reconstruction for discretized space derivatives. The proposed integration scheme for the Eulerian fluid equations is equivalent to a leapfrog scheme with an added higher order dissipative truncation errors. It can be used either as a much faster, yet of comparable accuracy, alternative to the PIC representation of plasma particle motion, or even in a hybrid fluid–particle combination when kinetic effects and particle injection and acceleration in a wakefield have to be investigated.