Mean Particle Velocity Research Articles

Динамика ансамбля активных броуновских частиц, управляемых шумом

Dynamics of an ensemble of small number of active Brownian particles is studied by means of numerical simulations. The particles are influenced by independent sources of noise, passive and active, and interact with each other through a global velocity field. We suppose that active noise affects to direction of the particle velocity only. Behaviour of the large ensemble and behaviour of the small one are compared. Mean velocity of particles of the large ensemble was analytically estimated earler. We show that a noise-induced "order- disorder" transition accompaniated by a bistability phenomena is observed in a small ensemble. A borderline of a coupling coefficient moves up while reducing the number of particles. Influence of passive noise leads to conversion of bistability to bimodality. There are two most probable values of a particle velocity in the last case. Borders of regions of bistability and bimodality are defined by the stochastic bifurcations of different kinds.

Virial pressure in systems of spherical active Brownian particles.

The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.

Giant enhancement of hydrodynamically enforced entropic trapping in thin channels

Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601 (2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and extensive Brownian dynamics simulations, we study particle transport through three-dimensional periodic channels of different height. Directed motion is caused by the interplay of constant bias acting along the channel axis and a pressure-driven flow. The tremendous change of the flow profile shape in channel direction with the channel height is reflected in a crucial dependence of the mean particle velocity and the effective diffusion coefficient on the channel height. In particular, we observe a giant suppression of the effective diffusivity in thin channels; four orders of magnitude compared to the bulk value.

An integrated multi-channel electrostatic sensing and digital imaging system for the on-line measurement of biomass–coal particles in fuel injection pipelines

The measurement of key parameters of biomass–coal particles in a pneumatic conveying pipeline at a power plant presents a significant challenge due to the inherent complexity of the dilute particle flow and differences in physical properties between the different kinds of fuels. This paper presents the latest development in on-line continuous measurement of mean particle velocity, concentration and particle size distribution of pulverised fuel using multi-channel electrostatic sensing and digital imaging techniques. An integrated instrumentation system has been implemented to achieve the intended measurement of pulverised fuel particles. Comprehensive tests were conducted on a 150mm bore horizontal pipe section of a large scale test facility using pulverised coal and biomass–coal blends. The results suggest that the characteristics of the pulverized fuel flow depend on the flow velocity and biomass proportion in the mixture and, to a large extent, on the biomass properties. It is found that coal particles travel faster and carry more electrostatic charge than biomass–coal blends. As more biomass particles (up to 20% by weight) are added to the flow, the particle velocity reduces, the electrostatic charge level decreases, and the flow becomes less stable in comparison with coal flow.

Velocity characterization of dense phase pneumatically conveyed solid particles in horizontal pipeline through an integrated electrostatic sensor

Dense phase pneumatic conveying of pulverized fuel particles under high pressure is one of the key techniques in large scale gasification of coal and petroleum coke. The real time and continuous measurement of dense phase gas–solid flow parameters such as particle velocity, concentration and mass flow rate has great significance for the in-depth understanding of particle flow dynamic behaviors and the optimized design of the conveying system. In this paper, an integrated electrostatic sensor is designed and used to explore the flow characteristics of anthracite and petroleum coke particles on a dense phase pneumatic conveyor. The ring electrodes in the integrated sensor are capable of measuring the “mean” velocity of solid particles over the whole cross-section of the pipeline, while the arc electrodes are employed to determine the local velocity of particles near them. The experimental results on a dense phase pneumatic conveyor under high pressure demonstrate that the flow characteristics depend on the physical properties of solid particles and carrying gas. Petroleum coke particles are much easier to be suspended in the gas flow than the anthracite particles, but its flow stability is worse. The local velocities from the arc electrode pairs mounted on the top of the pipeline are usually higher than those from the arc electrodes on the bottom for a stratified flow. The velocity from the ring electrode pair, indicating the mean velocity of particles over the whole cross-section, is usually higher than the local velocities from the arc electrode pairs for a suspension flow. In addition, the relationship between the mass flow rate and charge level of dense phase pneumatically conveyed solid particles is very complicated due to the complexity of the particle flow and the charge level cannot be used to measure particle concentration or mass flow rate.

Numerical study of particle behavior in laminar axisymmetric opposed-jet flows

The particle behavior in laminar axisymmetric opposed-jet flows is investigated numerically using a high order finite difference method and Lagrangian particle tracking. The deterministic hard-sphere collision model is used to deal with the inter-particle collisions, and the feedback of the particles on the carrier phase is neglected in the present work. In the scope of particle volume fractions and particle Stokes numbers studied, the particle collision rates in the impinging zone can agree with the prediction of cylinder formula (Saffman & Turner, 1956). The results found that inter-particle collisions have significant influence on particle distribution, velocities and residence time. When particle volume fraction at nozzle outlet is smaller than O(10−4), inter-particle collisions make little difference on the particle concentration profile, which is primarily decided by the maximum penetration distance (MPD) of a particular particle. Particle will prefer to concentrate at the location of MPD when the MPD is within the flow domain, otherwise particles will evenly distribute along the axis of two nozzles. When particle volume fraction is higher than O(10−3), the effect of inter-particle collisions become significant, which can impede particles reaching the MPD so that particles will prefer to concentrate at the impinging plane. Inter-particle collisions can restrain the penetration process of particles, and shorten the particle residence time at the same time. Due to massive collisions, particle mean velocity profile has the similar shape with the profile of gas velocity in the impinging zone, and slip velocity between particles and gas will be decreased.

Shape of scoria cones on Mars: Insights from numerical modeling of ballistic pathways

Morphological observations of scoria cones on Mars show that their cross-sectional shapes are different from those on Earth. Due to lower gravity and atmospheric pressure on Mars, particles are spread over a larger area than on Earth. Hence, erupted volumes are typically not large enough for the flank slopes to attain the angle of repose, in contrast to Earth where this is common. The distribution of ejected material forming scoria cones on Mars, therefore, is ruled mainly by ballistic distribution and not by redistribution of flank material by avalanching after the static angle of repose is reached. As a consequence, the flank slopes of the Martian scoria cones do not reach the critical angle of repose in spite of a large volume of ejected material. Therefore, the topography of scoria cones on Mars is governed mainly by ballistic distribution of ejected particles and is not influenced by redistribution of flank material by avalanching. The growth of a scoria cone can be studied numerically by tracking the ballistic trajectories and tracing the cumulative deposition of repeatedly ejected particles. We apply this approach to a specific volcanic field, Ulysses Colles on Mars, and compare our numerical results with observations. The scoria cones in this region are not significantly affected by erosion and their morphological shape still preserves a record of physical conditions at the time of eruption. We demonstrate that the topography of these scoria cones can be rather well (with accuracy of ∼10 m) reproduced provided that the ejection velocities are a factor of ∼2 larger and the ejected particles are about ten times finer than typical on Earth, corresponding to a mean particle velocity of ∼92 m/s and a real particle size of about 4 mm. This finding is in agreement with previous theoretical works that argued for larger magma fragmentation and higher ejection velocities on Mars than on Earth due to lower gravity and different environmental conditions.

Impurities as a quantum thermometer for a Bose-Einstein condensate

We introduce a primary thermometer which measures the temperature of a Bose-Einstein Condensate in the sub-nK regime. We show, using quantum Fisher information, that the precision of our technique improves the state-of-the-art in thermometry in the sub-nK regime. The temperature of the condensate is mapped onto the quantum phase of an atomic dot that interacts with the system for short times. We show that the highest precision is achieved when the phase is dynamical rather than geometric and when it is detected through Ramsey interferometry. Standard techniques to determine the temperature of a condensate involve an indirect estimation through mean particle velocities made after releasing the condensate. In contrast to these destructive measurements, our method involves a negligible disturbance of the system.

Ratcheting of Brownian swimmers in periodically corrugated channels: a reduced Fokker-Planck approach.

We consider the motion of self-propelling Brownian particles in two-dimensional periodically corrugated channels. The point-size swimmers propel themselves in a direction which fluctuates by Brownian rotation; in addition, they undergo Brownian motion. The impermeability of the channel boundaries in conjunction with an asymmetry of the unit-cell geometry enables ratcheting, where a nonzero particle current is animated along the channel. This effect is studied here in the continuum limit using a diffusion-advection description of the probability density in a four-dimensional position-orientation space. Specifically, the mean particle velocity is calculated using macrotransport (generalized Taylor-dispersion) theory. This description reveals that the ratcheting mechanism is indirect: swimming gives rise to a biased spatial particle distribution which in turn results in a purely diffusive net current. For a slowly varying channel geometry, the dependence of this current upon the channel geometry and fluid-particle parameters is studied via a long-wave approximation over a reduced two-dimensional space. This allows for a straightforward seminumerical solution. In the limit where both rotational diffusion and swimming are strong, we find an asymptotic approximation to the particle current, scaling inversely with the square of the swimming Péclet number. For a given swimmer-fluid system, this limit is physically realized with increasing unit-cell size.

Local Particle Mean Velocity Measurement in Pneumatic Conveying Pipelines Using Electrostatic Sensor Arrays

In this paper, a measurement system for the local mean velocity of pneumatically conveyed particles is proposed and developed. It mainly consists of electrostatic sensor arrays, signal conditioning circuits, and a digital signal processor (DSP)-based data acquisition and processing unit. Electrostatic sensor arrays are used to detect the charge on particles in its sensing zone and further make the local particle mean velocity measurement in conjunction with cross-correlation method. The sampling frequency is determined from theoretical analysis of the bandwidth of electrostatic signal and accuracy of correlation velocity calculation. Experiments are carried out on a belt conveyor and a gravity-fed particle rig to determine the optimized sampling number of the electrostatic signal through analyzing the measurement error of the transit time. The results showed that the more sampling numbers, the higher stability of measurement results. The repeatability of the measurement system is less than ±2.2% and the linearity is better than ±4.9% over the velocity range of 5.50–21.98 m/s. Experiments are also performed on a high-pressure dense-phase pneumatic conveying system of pulverized coal, indicating that the measurement system is capable of achieving local mean velocity measurement of pneumatically conveyed particles with the relative standard deviation less than 5.5%.

Simulation of Wood Particle Motion Through a Concurrent Triple-Pass Rotary Dryer

The retention time of solids in a drum is an important parameter for the design of rotary dryers, since it directly influences the mass and heat transfer rates. If it is too short, the wood particles do not become adequately dried. If it is too long, they become over-dried. Therefore, having an appropriate retention time is useful in terms of both energy and plant capacity. Wood particle mean retention time in a rotary dryer is affected by several variables, such as dryer dimensions, solid characteristics, and operational parameters. The purpose of this work was to simulate the effects of some wood particle characteristics and operational parameters on the mean retention time, drum holdup, and velocity of the wood particles during drying in a pilot-scale, closed-loop, triple-pass rotary dryer by means of a computer code. The simulation results of wood particle motion can be used for modeling, design, and optimization of closed-loop, triple-pass rotary dryers.

Effect of Reloading on Dynamic Recrystallization in Shock Deformed Aluminum Alloy

In order to verify influence of particle velocity non-uniformity on dynamic recrystallization (DRX), shock tests of D16 Al alloy were conducted under uniaxial strain conditions within strain-rate range of 105 ÷ 107 s-1. The particle velocity non-uniformity arises due to both initial heterogeneity and non-linearity of shock-wave process. Apart from the nature of DRX mechanism, migrational or rotational, the particle velocity non-uniformity facilitates growth of local strain, strain rate and temperature. To adjust a duration of the particle velocity non-uniformity degree, two limiting situations is provided by means of single and double shock loading (reloading). The experimental technique used allows to register both mean particle velocity profile and particle velocity variation which is the quantitative characteristic of velocity non-uniformity. Shock tests of D16 Al alloy in single and reloading regimes [ show that dynamic recrystallization takes place only in the second case. The reloading regime initiates a ten-fold increase in duration of the particle velocity non-uniformity stage, which is sufficient for fulfillment of the well-known DRX conditions: γ 3, dγ/dt 104 s1, T 0.4Tm. The regions of DRX with equal-axis grains of ~1 μm in diameter are revealed with the metallography and X-ray analysis.

Spatial filtering characteristics of electrostatic sensor matrix for local velocity measurement of pneumatically conveyed particles

The accuracy of local particle mean velocity measurement with spatial filtering method based on an electrostatic sensor matrix (ESM) is closely related to its sensitivity and spatial filtering characteristics. In this paper, the three-dimensional electrostatic field generated by a point charge in the sensing zone of the ESM is solved by using a finite element method to obtain the spatial sensitivity distributions of the ESM. Further a dimensionless calculation model for the sensitivity of the ESM is suggested based on a Cosine function. The numerical results demonstrate that the spatial sensitivity has a periodic distribution along the axial direction and its spatial periodicity is determined by the axial spacing between two adjacent electrodes. The sensitivity over the central cross-section is localized. The spatial filtering characteristics of the ESM are also investigated and verified by experiments on a gravity-fed rig. These results provide a basis for the optimized design of the ESM.

Surface slopes, velocity profiles and fluid pressure in coarse-grained debris flows saturated with water and mud

AbstractData on the internal velocity distribution of flowing sediment–fluid mixtures such as debris flows are rare, but necessary for model development and testing. A probe to measure the mean particle velocity at different depths and different locations within experimental debris flows in a 4 m diameter rotating drum was developed. In addition, the flow depth, basal normal stress and basal pore fluid pressure were also measured. Results show that for a given sediment–fluid mixture the velocity profiles collapse to distinct non-dimensional profiles. Macroscopic flow behaviour shows great similarity, with mean surface slopes weakly dependent on the shear rate for water-saturated gravel, but strongly shear-rate-dependent when pores are filled with mud. Poorly sorted material with a high content of fines produced fluid pressures close to normal stress and sidewall friction had a strong effect on the flow pattern. Our results reveal variability in profile characteristics for flows displaying similar macro-dynamics and provide data for model testing.

Prediction of a particle-laden turbulent channel flow: Examination of two classes of stochastic dispersion models

Nowadays, two families of stochastic models are mainly used to predict the dispersion of inertial particles in inhomogeneous turbulent flows. This first one is named “normalized model” and the second one “Generalized Langevin Model (GLM)”. Nevertheless, the main differences between the normalized and GLM models have not been thoroughly investigated. Is there a model which is more suitable to predict the particle dispersion in inhomogeneous turbulence? We propose in the present study to clarify this point by computing a particle-laden turbulent channel flow using a GLM-type model, and also a normalized-type model. Particle statistics (such as concentration, mean and rms particle velocity, fluid-particle velocity covariances) will be provided and compared to Direct Numerical Simulation (DNS) data in order to assess the performance of both dispersion models. It will be shown that the normalized dispersion model studied can predict correctly the effect of particle inertia on some dispersion statistics, but not on all. For instance, it was found that the prediction of the particle kinetic shear stress and some components of the fluid-particle covariance is not physically acceptable.

Dense suspension of solid particles as a new heat transfer fluid for concentrated solar thermal plants: On-sun proof of concept

This paper demonstrates the capacity of dense suspensions of solid particles to transfer concentrated solar power from a tubular receiver to an energy conversion process by acting as a heat transfer fluid. Contrary to a circulating fluidized bed, the dense suspension of particles’ flows operates at low gas velocity and large solid fraction. A single-tube solar receiver was tested with 64µm mean diameter silicon carbide particles for solar flux densities in the range 200–250kW/m2, resulting in a solid particle temperature increase ranging between 50°C and 150°C. The mean wall-to-suspension heat transfer coefficient was calculated from experimental data. It is very sensitive to the particle volume fraction of the suspension, which was varied from 26 to 35%, and to the mean particle velocity. Heat transfer coefficients ranging from 140W/m2K to 500W/m2K have been obtained, thus corresponding to a 400W/m2K mean value for standard operating conditions (high solid fraction) at low temperature. A higher heat transfer coefficient may be expected at high temperatures because the wall-to-suspension heat transfer coefficient increases drastically with temperature. The suspension has a heat capacity similar to a liquid heat transfer fluid, with no temperature limitation but the working temperature limit of the receiver tube. Suspension temperatures of up to 750°C are expected for metallic tubes, thus opening new opportunities for high efficiency thermodynamic cycles such as supercritical steam and supercritical carbon dioxide.

An investigation of the generation of Acoustic Emission from the flow of particulate solids in pipelines

This paper is concerned with the generation of the Acoustic Emission (AE) from particulate flow and an investigation of the potential of implementing AE for flow parameters, namely the solid mass flow rate, particle velocity and size, monitoring. A series of experiments has been conducted to gather AE signals from a laboratory scale single flow-loop pneumatic conveying system. Initially, AE sensors were attached to two steel meshes which were placed with a fixed axial distance in the pipeline to study the generation of the AE and subsequently the possibility of using those generated AE to determine particle velocity in the pipeline. Particle velocities measured from this approach were compared with theoretical predictions. The results indicated that this approach could measure the mean particle velocity with reasonable accuracy. The generation of AE on five different sensor mounting locations was also studied. The results showed that sensors mounted on all those locations were able to respond to changes in the flow parameters. However, only two sensor locations (outer bend and Mesh) were chosen for further investigation. The final experimental results indicated that the AE features, namely Root-Mean-Square (RMS) and energy of the AE, are related to the changes in the flow parameters and good correlations were found. Good correlations between the RMS and energy of the AE with the momentum and kinetic energy of the particles, respectively, were also found. Overall, the studies indicated that features of AE have great potential in gas–solid two phase flow parameter monitoring. However, the studies also show that the applicability of the AE techniques to measure solid mass flow rates in practice would require tedious calibration.

GPU-based discrete element simulation on a tote blender for performance improvement

The mixing and flow of granular materials in a conical tote blender are investigated using a GPU-based DEM software to explore new approaches to enhance mixing. The structure and dimensions of the blender and other simulation conditions are set according to experimental data from literature. A parametric study on fill level and rotation rate is carried out from which optimum values are found with respect to mixing rate, productivity and energy consumption. It is also found that the standard horizontal installation of the blender results in poor axial mixing, while inclining the blender at a certain angle can enhance mixing effectively. This may be ascribed to the larger mean particles velocity and better velocity distribution under such conditions, which is confirmed to be a consistent character for relatively large-scale systems. Furthermore, the effect of operating conditions for the inclined blender is also examined. It is close to those for the standard blender but has less effect on mixing rate. Inclining the blender at a certain angle is found to be an effective and simple approach to speed up mixing especially if the inclining angle varies from 30 to 60°. This may be ascribed to the larger mean particle velocity and better velocity distribution under such conditions which are confirmed to be consistent character for relatively large-scale systems. ► We explore new approaches to enhance mixing for a conical tote blender. ► The optimal fill level and rotation rate are found with respect to industrial demand. ► Inclined the blender at a certain angle can enhance mixing effectively. ► We optimize the inclined angle. ► We examine the effect of the inclined angle on axial and radial particle velocities.

Higher order statistical analysis of Eulerian particle velocity data in CFB risers as measured with high speed particle imaging

Velocities of individual particles have been measured in gas-particle flow fields within the risers of two circulating fluidized bed (CFB), one with a 0.305 m diameter riser at the National Energy Technology Laboratory (NETL) and one with a 0.20 m diameter riser at Particle Solid Research Inc. (PSRI). The risers were operated at moderate to high particle concentrations (solid fluxes up to 400 kg/m2s). The NETL riser was operated in the core–annulus regime. The PSRI riser was operated in both the core–annulus and dense up-flow regimes. HDPE particles with a mean diameter of 800 μm were used in the NETL riser and FCC particles with a mean diameter of 80 μm were used in the PSRI riser. Particle velocities were measured with a high speed particle imaging velocimetry (HSPIV) system developed by the NETL. The HSPIV measurement technique has the ability to measure the velocities and trajectories of thousands of particles simultaneously in flows of high particle concentration. In this study, particle velocities are measured in a small two-dimensional field-of-view with dimensions in the range of 1–5 mm wide by 1–10 mm high, with a depth of about 1 mm. The size of the field-of-view is chosen to be similar to the size of CFD grid cells in models used by NETL and small enough that gradients of the mean particle velocity are small over the field-of-view, but large enough to achieve high data sample rates (at least ten velocity vectors per camera frame). In this study sample rates for particle velocity vectors were in the range of 0.1 to 1 million per second. This sample rate provides the high temporal resolution necessary to resolve the complete temporal domain of particle velocity. Particle velocities in each camera frame (at each point in time) are averaged to yield a pointwise instantaneous particle velocity. Using a recently developed particle velocity decomposition technique (Gopalan and Shaffer, 2011 [15]) the pointwise particle velocity time series is decomposed into a varying mean Eulerian component and a random fluctuating component. Statistics of the Eulerian velocity, namely the mean, RMS, skewness and kurtosis, and the granular temperature of the random fluctuating component are presented in this study. Results show that the vertical component of the overall mean Eulerian velocity decreases with increasing mass flux in both the core–annulus and dense up-flow regimes. The root mean square (RMS) of the Eulerian velocity in the horizontal direction is independent of the radial location in the NETL riser. In the PSRI riser, for both the core–annulus and dense upflow regime, the RMS of the horizontal Eulerian velocity decreases monotonically from the center of the riser to the wall. The radial profile of the RMS of the vertical Eulerian velocity for the PSRI riser is parabolic with a peak near r/R ~ 0.5–0.6 for the dense upflow regime. For the core–annulus regime the radial profile of the RMS of the vertical Eulerian velocity is relatively flat for both the NETL and PSRI risers, with a slight decrease near the wall in the PSRI riser. The skewness of the PDF of Eulerian velocity is near zero in the horizontal direction for the dense upflow regime in the PSRI riser, the only Eulerian velocity distribution for which the Gaussian approximation is appropriate. The skewness trends of the vertical velocity distribution are more complex and require further experimental confirmation. The kurtosis of the PDF of the Eulerian velocity is always higher in the horizontal direction than the vertical direction except at the wall of the riser. The 80 μm FCC particles in the PSRI riser showed much higher granular temperature than the 800 μm particles in the NETL riser. The granular temperature decreases monotonically for all conditions from the center of the riser to the wall. granular temperature is anisotropic for all conditions in both risers. The radial profile of anisotropy of granular temperature is relatively flat over most of the NETL and PSRI risers with values in the range of 0.3 to 0.6. Near the wall it decreases for the PSRI riser, while increasing for the NETL riser.

Evaluation of the saltation process of bed materials by video imaging under altered bed roughness

ABSTRACTThe purpose of this paper is to examine the nature of particle saltation and movement over the beds of fixed roughness from flume experiments. A series of experiments are carried out to study the saltation of individual sand particles of different sizes over rough beds under different flow conditions. A 3‐D acoustic Doppler velocimeter is used to record the fluid velocity components; subsequently, under different flow conditions, the images of released sand particles are recorded using high‐speed video imaging technique. Systematic analysis is made with regard to the forces acting on the grains and the variation of their magnitudes along the saltation trajectories of the grains. Relations between the saltation parameters, flow intensity and bed roughness are developed. The distributions of the angle of orientations during a single saltation follows almost a Gaussian distribution. The shape of the Gaussian distribution depends on the particle size and bed roughness. Particle collisions with rough beds and the resulting coefficients of restitution are also discussed. A theoretical framework is developed to compute the mean particle velocity considering the spin in the energy balance equation. Results of the detailed analysis using the imaging technique are much better than in previously reported studies. Copyright © 2013 John Wiley & Sons, Ltd.