Particle Velocity Variance Research Articles

Shock-induced structural instability and dynamic strength of metals

The shock tests of set of metals show that together with well-known dynamic strength-characteristics of material such as dynamic yielding limit and spall strength, the additional characteristics, namely, threshold of structural instability under shock compression, defect of the velocity at the plateau of compressive pulse and particle velocity variance at the mesoscale should be introduced into analysis of dynamic strength of materials. The structural instability threshold registered in uniaxial strain conditions allows the resistance to penetration in Tate-Alekseevskii equation to be determined.

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.

Stochastic particle based models for suspended particle movement in surface flows

Modeling of suspended sediment particle movement in surface water can be achieved by stochastic particle tracking model approaches. In this paper, different mathematical forms of particle tracking models are introduced to describe particle movement under various flow conditions, i.e., the stochastic diffusion process, stochastic jump process, and stochastic jump diffusion process. While the stochastic diffusion process can be used to represent the stochastic movement of suspended particles in turbulent flows, the stochastic jump and the stochastic jump diffusion processes can be used to describe suspended particle movement in the occurrences of a sequence of extreme flows. An extreme flow herein is defined as a hydrologic flow event or a hydrodynamic flow phenomenon with a low probability of occurrence and a high impact on its ambient flow environment. In this paper, the suspended sediment particle is assumed to immediately follow the extreme flows in the jump process (i.e. the time lag between the flow particle and the sediment particle in extreme flows is considered negligible). In the proposed particle tracking models, a random term mainly caused by fluid eddy motions is modeled as a Wiener process, while the random occurrences of a sequence of extreme flows can be modeled as a Poisson process. The frequency of occurrence of the extreme flows in the proposed particle tracking model can be explicitly accounted for by the Poisson process when evaluating particle movement. The ensemble mean and variance of particle trajectory can be obtained from the proposed stochastic models via simulations. The ensemble mean and variance of particle velocity are verified with available data. Applicability of the proposed stochastic particle tracking models for sediment transport modeling is also discussed.

Radiation from a varying velocity charge in flight through a plate

The radiation from a particle traversing with varying velocity through a plate in straight motion (along the normal to its surface) has been investigated. It is assumed that the particle coordinate (inside the plate) is an arbitrary monotone function of time. The calculations are based on appropriate exact solutions of the Maxwell equations. It was shown that as a result of variation of particle velocity inside the plate (e.g., due to its slowing-down) the spectral-angular distribution of Cherenkov radiation generated by the particle inside the plate may be essentially affected. Possible practical application of this phenomenon is discussed.

Shock wave propagation in layered planetary embryos

The propagation of impact-induced shock wave inside a planetary embryo is investigated using the Hugoniot equations and a new scaling law, governing the particle velocity variations along a shock ray inside a spherical body. The scaling law is adopted to determine the impact heating of a growing embryo in its early stage when it is an undifferentiated and uniform body. The new scaling law, similar to other existing scaling laws, is not suitable for a large differentiated embryo consisting of a silicate mantle overlying an iron core. An algorithm is developed in this study on the basis of the ray theory in a spherically symmetric body which relates the shock parameters at the top of the core to those at the base of the mantle, thus enabling the adoption of scaling laws to estimate the impact heating of both the mantle and the core. The algorithm is applied to two embryo models: a simple two-layered model with a uniform mantle overlying a uniform core, and a model where the pre-shock density and acoustic velocity of the embryo are radially dependent. The former illustrates details of the particle velocity, shock pressure, and temperature increase behind the shock front in a 2D axisymmetric geometry. The latter provides a means to compare the results with those obtained by a hydrocode simulation. The agreement between the results of the two techniques in revealing the effects of the core–mantle boundary on the shock wave transmission across the boundary is encouraging.

Dispersion in particle velocity resulting from random motion through a spatially-varying fluid velocity field in a pipe

Abstract A macro-scale probabilistic model of dilute phase pneumatic transport is developed to analyse the dispersion in the velocity of conveyed particles and to predict their velocity statistics. Fluid drag force, proportional to the relative velocity between the particle and fluid, is taken to be the agent that causes particle motion in the axial direction. The basic premise of the approach is that dispersion in axial particle velocity is a result of subsidiary random motion in the radial direction through the fluid velocity field. Two causes are investigated for this radial motion; gravity and inter-particle collisions. As the local fluid velocity experienced by a particle thus continuously varies in an unpredictable fashion, then the associated drag force fluctuates as does the resulting particle velocity. The non-deterministic nature of the fluid velocity acting on the particle is captured by treating fluid velocity as a stochastic process whose description comes from combining knowledge of the flow field with the nature of the radial motion of the particle. This novel approach allows analytical expressions to be obtained for the mean and variance of particle velocity. The accuracy of these predictions was checked by numerical simulation and found to be good. The analysis demonstrates that dispersion in particle velocity is a function of the magnitude of dispersion in fluid velocity (a fluid property), on the inertial rate constant of the particle (a combined particle/fluid property) and the autoregressive parameter (a property reflecting the type of radial motion).

A computational study of the role of particle size standard deviation on the collision frequency in differential settling

The results of a simple computational model for differential settling are presented illustrating the significant role that particle size distribution plays in collision frequency and sedimentation rate of particles in a quiescent environment. The model tracks a large number of particles (order 105) with log-normally distributed diameters, as they settle at their Stokes settling velocities. Particle collisions are detected and result in larger particles that fall more rapidly. A number of simplifying assumptions are made in the model in order to avoid empirical correlations for phenomena such as collision efficiency and particle shape. These simplifying assumptions were needed to isolate and quantify the role of the particle size distribution. Simulated concentration profiles indicate that, even in the absence of collisions, the standard deviation (σD) of the particle size strongly influences the bulk mass settling rate as, for larger σD, more mass is concentrated in larger, faster falling particles. The collision frequency is also a strong function of σD. For a given mass concentration the collision frequency first increases linearly with increasing σD as greater variation in particle size leads to greater variation in particle velocity, and shorter times for particles to catch each other. For larger σD more mass is concentrated in larger particles, so, for a given mass concentration, there are fewer particles per unit volume, increasing the mean distance between the particles and reducing the collision frequency. The implications of these results for sedimentation measurement using optical attenuation techniques are discussed.

Particle Dispersion Behaviors of Dense Gas-Particle Flows in Bubble Fluidized Bed

An Euler-Euler two-fluid model incorporating a developed momentum transfer empirical coefficient is developed to study the particle dispersion behaviors of dense gas-particle flows in gas-fluidization reactor. In this model, the four-way couplings among gas-particles, particle-gas, and particle-particle collisions are fully considered based on kinetic theory of granular flows and an improved smooth continuous drag coefficient is utilized. Gas turbulent flow is solved by large eddy simulation. The particle fraction, the time-averaged axial particle velocity, the histogram of particle fluctuation velocity, and the wavelet analysis of pressure signals are obtained. The results are in good agreement with experimental measurements. The mean value and the variance of axial particle velocity are greater than those of radial particle velocities. Particle collision frequencies at bubble vibrant movement regions along axial direction are much higher than those of radial direction and attenuated along height increase. Low-frequency component of pressure signal indicating the bubble movement behaviors in the center of reactor is stronger than wall regions. Furthermore, the negative values represent the passed bubble and positive peak values disclose the continuous motion of single bubble.

Selective particle and cell clustering at air–liquid interfaces within ultrasonic microfluidic systems

In this study, we demonstrate particle and cell clustering in distinct patterns on the free surface of microfluidic volumes. Employing ultrasonic actuation, submersed microparticles are forced to two principal positions: nodal lines (pressure minima) of a standing wave within the liquid bulk, and distinct locations on the air–liquid interface (free surface); the latter of which has not been previously demonstrated using ultrasonic standing waves. As such, we unravel the fundamental mechanisms behind such patterns, showing that the contribution of fluid particle velocity variations on the free surface (acoustic radiation force) results in patterned particle clustering. In addition, by varying the size and density of the microparticles (3.5–31 μm polystyrene and 1–5 μm silica), acoustic streaming is found to increase the tendency for a smaller and lighter particle to cluster at the air–liquid interface. This selectivity is exploited for the isolation of multiple microparticle and cell types on the free surface from their nodally aligned counterparts. Free surface clustering is demonstrated in both an open microfluidic chamber and a sessile droplet, as well as using a range of biological species Escherichia coli, blood cells, Ragweed pollen and Paper Mulberry pollen). The ability to selectively cluster submersed microparticles and cells in distinct patterns on the free surface showcases the excellent suitability of this method to lab-on-a-chip systems.

Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence

We study by means of an Eulerian–Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, besides added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force–known as Basset–Boussinesq history force–and the non-Stokesian drag based on Schiller–Naumann parametrization, together with the finite-size Faxén corrections. We focus on the case of flow at low Taylor–Reynolds number, R e λ ≃ 31 , for which fully resolved numerical data which can be taken as a reference are available [Homann H., Bec J. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J Fluid Mech 651 (2010) 81–91]. Remarkably, we show that while drag forces have always minor effects on the acceleration statistics, their role is important on the velocity behavior. We propose also that the scaling relations for the particle velocity variance as a function of its size, which have been first detected in fully resolved simulations, does not originate from inertial-scale properties of the background turbulent flow but it is likely to arise from the non-Stokesian component of the drag produced by the wake behind the particle. Furthermore, by means of comparison with fully resolved simulations, we show that the Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particles whose size attains the integral scale.

Doppler velocimetry on microparticles trapped and propelled by laser light in liquid-filled photonic crystal fiber

Laser Doppler velocimetry is used to measure very accurately the velocity and position of a microparticle propelled and guided by laser light in liquid-filled photonic crystal fiber. Periodic variations in particle velocity are observed that correlate closely with modal beating between the two lowest order guided fiber modes.

Deformation of compliant fault zones induced by nearby earthquakes: Theoretical investigations in two dimensions

[1] Using spontaneous rupture models with off-fault elastoplastic material response, we investigate the deformation of compliant fault zones induced by nearby earthquake ruptures in a two-dimensional plane-strain framework. We find that dynamic stresses from nearby ruptures can produce inelastic strain along some portions of a fault zone that experience dilatational stress changes, if the fault zone rock is close to failure in the prestress field. Accumulation of inelastic strain causes dramatic variations in particle velocity across the fault zone, reversing the sense of fault-parallel relative motion from retrograde (opposite to the long-term geologic slip) to sympathetic (consistent with the long-term slip) during the dynamic process. In the static displacement field of a roughly parallel strike-slip fault system, the inelastic response of a fault zone results in sympathetic motion, while the elastic response generally gives rise to retrograde motion. Our theoretical investigations reveal that some deficiencies may exist in applying an elastic inhomogeneity model to infer fault zone properties in previous studies, including the assumption of negligible fault-normal motion and ignorance of changes in some components of the stress tensor. These deficiencies and possible constraints on the in situ stress state by inelastic strain signals in the static displacement field call for a reexamination of existing observations of fault zone deformation induced by recent large earthquakes.

Study on Process Optimization of Cold Gas Spraying

Cold gas dynamic spraying is a relatively new spray coating technique capable of depositing a variety of materials without extensive heating. As a result the inherent degradation of the powder particles found during traditional thermal spraying can be avoided. The simplicity of this technique is its most salient feature. High pressure gas is accelerated through a convergent-divergent nozzle up to supersonic velocity. The powder particles are carried to the substrate by the gas and on impact the particles deform at temperatures below their melting point. Computational modeling of thermal spray systems can provide thorough descriptions of the complex, compressible, particle-laden flow, and therefore can be utilized to strengthen understanding and allow technological progress to be made in a more systematic fashion. The computational fluid dynamic approach is adopted in this study to examine the effects of changing the nozzle cross-section shape, particle size and process gas type on the gas flow characteristics through a cold spray nozzle, as well as the spray distribution and particle velocity variation at the exit.

Hydrodynamic behavior of dense gas-particle flows under the reduced gravity conditions

An Euler–Euler two-fluid model incorporating with the influence of gravity to describe the hydrodynamic behavior of dense gas-particle flows in gas-fluidization reactor is presented and simulated numerically. It based on the dense gases of kinetic theory and the kinetic theory of granular media for considering the interactions between particle–particle and gas-particles. Gas turbulent flow is solved by large eddy simulation. Results showed that the mean value and the variance of vertical particle velocity are greater than those of horizontal velocity under both lunar-reduced and earth gravity conditions. Comparison of the earth gravity, reduced condition is easier to produce the bigger volume bubble and the more heterogeneous flow structure, as well as the greater the variance of vertical and horizontal particle velocity and the higher particle fluctuation intensity.

Particle velocity models for ultra-high pressure abrasive waterjets

Particle velocity and trajectory in an ultra-high pressure abrasive waterjet (AWJ) are important jet characteristic information required for understanding and modelling the particle erosion process involved in AWJ machining. In this paper, mathematical models for the particle velocity variations across and along an AWJ are developed based on an in-depth understanding of the jet dynamic characteristics from a computational fluid dynamics (CFD) simulation study. The models are then assessed qualitatively and quantitatively. It is found that the model predictions are reasonable and consistent with the data from a verified CFD model with an average percentage error of less than 1%.

Velocity fluctuations and hydrodynamic diffusion in finite-Reynolds-number sedimenting suspensions

The velocity variance and the hydrodynamic diffusivity for a finite-Reynolds-number settling suspension are determined from lattice-Boltzmann simulations of many particles in cubic cells with periodic boundary conditions. The velocity variance is found to grow logarithmically with the size of the computational domain in contrast to the algebraic growth found in comparable Stokes-flow simulations. The growth rate and size of the velocity variance are found to be smaller than the theoretical prediction for a random suspension owing to a deficit in particle pair probability distribution in the wake of a test particle that screens the velocity disturbance felt by other particles. The particle velocity variance is smaller than the fluid velocity variance because a particle does not follow fluid motions on length scales comparable to or smaller than its own size. The hydrodynamic diffusivity of particles is proportional to the product of the root-mean-square velocity and the size of the computational domain.

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate calculation of the interphase momentum transfer term in LE simulations is crucial for predicting qualitatively correct physical behavior, as well as for quantitative comparison with experiments. Numerical error in the interphase momentum transfer calculation arises from both forward interpolation/approximation of fluid velocity at grid nodes to particle locations, and from backward estimation of the interphase momentum transfer term at particle locations to grid nodes. A novel test that admits an analytical form for the interphase momentum transfer term is devised to test the accuracy of the following numerical schemes: (1) fourth-order Lagrange Polynomial Interpolation (LPI-4), (3) Piecewise Cubic Approximation (PCA), (3) second-order Lagrange Polynomial Interpolation (LPI-2) which is basically linear interpolation, and (4) a Two-Stage Estimation algorithm (TSE). A number of tests are performed to systematically characterize the effects of varying the particle velocity variance, the distribution of particle positions, and fluid velocity field spectrum on estimation of the mean interphase momentum transfer term. Numerical error resulting from backward estimation is decomposed into statistical and deterministic (bias and discretization) components, and their convergence with number of particles and grid resolution is characterized. It is found that when the interphase momentum transfer is computed using values for these numerical parameters typically encountered in the literature, it can incur errors as high as 80% for the LPI-4 scheme, whereas TSE incurs a maximum error of 20%. The tests reveal that using multiple independent simulations and higher number of particles per cell are required for accurate estimation using current algorithms. The study motivates further testing of LE numerical methods, and the development of better algorithms for computing interphase transfer terms.

Simulation of granular flow in 2-D hoppers using the Caram–Hong model

The Caram–Hong stochastic model for granular motion in hoppers or silos was applied, with minor modification, to describe the flow of particles in 2D batch hoppers. The predictions of the model were compared to experimental measurements, made by particle image velocimetry, on a laboratory hopper containing zinc particles. With respect to both the spatial variation of particle velocity and the rate of descent of the top surface of the bed, the model showed satisfactory agreement with the experimental data.

AN IMPROVEMENT TO THE SSF MODEL FOR PREDICTION OF LIGHT PARTICLE DISPERSION

This study investigates the predicted motion of small, light particles using the stochastic separated flow models proposed by Shuen et al. (1983) and Lightstone and Raithby (1998). Model predictions are compared to the benchmark experiment of Snyder and Lumley (1971) for particles released from a point source in grid-generated turbulence. It is found that the predictions of particle velocity variance and dispersion exhibit nonphysical waves. This behavior is explored in order to understand its mathematical basis arising from the model formulation. A modification to the model is presented. The modified model is successful in removing the characteristic waves.

Time scales for predicting dispersion of arbitrary-density particles in isotropic turbulence

The effects of particle inertia and particle-to-fluid density on the time scales that measure the dispersion of particles by isotropic turbulence are investigated. Numerical calculations are performed by means of a kinematic simulation method coupled with Lagrangian tracking of discrete particles. Moreover, a simple semi-empirical model for predicting the time scales of the fluid velocity seen by a particle as well as of the fluid–particle velocity covariance and the particle velocity variance is proposed. Comparisons between simulations and model predictions are presented.