Particle Velocity Variance Research Articles

LES–DPS of the effect of wall roughness on dispersed-phase transport in particle-laden turbulent channel flow

The influence of wall roughness on dispersed-phase properties of particle-laden turbulent channel flow is investigated using large eddy simulation (LES) for the fluid flow and discrete particle simulation (DPS) for the particulate phase. Gas–solid flows are considered for which the particle equation of motion includes the contribution from the drag force. The influence of wall roughness is treated stochastically in which the impact angle is comprised of the particle trajectory angle and a stochastic component due to wall roughness. Elastic particle–wall collisions are considered with surface roughness characterized in terms of the standard deviation of the distribution of wall roughness angles. Computations are performed for three Stokes numbers and standard deviations in the wall roughness angle of 0 (smooth wall), 2.5° and 5°. LES–DPS results show that for a given wall roughness angle and particle Stokes number the most pronounced effect is on the wall-normal component of the particle velocity, which can be substantially increased by roughness. While the streamwise particle velocity variance also increases, the spanwise particle fluctuating velocity exhibits relatively little sensitivity to surface roughness. In addition, LES/DPS results show that wall roughness increases turbulent transport of the wall-normal particle velocity variance, in turn providing a mechanism for elevation of the particle velocity fluctuations across the entire flow.

Dynamic behavior of boron carbide

Boron carbide displays a rich response to dynamic compression that is not well understood. To address poorly understood aspects of behavior, including dynamic strength and the possibility of phase transformations, a series of plate impact experiments was performed that also included reshock and release configurations. Hugoniot data were obtained from the elastic limit (15–18 GPa) to 70 GPa and were found to agree reasonably well with the somewhat limited data in the literature. Using the Hugoniot data, as well as the reshock and release data, the possibility of the existence of one or more phase transitions was examined. There is tantalizing evidence, but at this time no phase transition can be conclusively demonstrated. However, the experimental data are consistent with a phase transition at a shock stress of about 40 GPa, though the volume change associated with it would have to be small. The reshock and release experiments also provide estimates of the shear stress and strength in the shocked state as well as a dynamic mean stress curve for the material. The material supports only a small shear stress in the shocked (Hugoniot) state, but it can support a much larger shear stress when loaded or unloaded from the shocked state. This strength in the shocked state is initially lower than the strength at the elastic limit but increases with pressure to about the same level. Also, the dynamic mean–stress curve estimated from reshock and release differs significantly from the hydrostate constructed from low-pressure data. Finally, a spatially resolved interferometer was used to directly measure spatial variations in particle velocity during the shock event. These spatially resolved measurements are consistent with previous work and suggest a nonuniform failure mode occurring in the material.

1023 金属材料内の衝撃波伝播に伴う粒子速度変化の数値予測

1023 金属材料内の衝撃波伝播に伴う粒子速度変化の数値予測

Doppler Cloud Radar Derived Drop Size Distributions in Liquid Water Stratus Clouds

A cloud particle size retrieval algorithm that uses radar reflectivity factor and Doppler velocity obtained by a 35-GHz Doppler radar and liquid water path estimated from microwave radiometer radiance measurements is developed to infer the size distribution of stratus cloud particles. Assuming a constant, but unknown, number concentration with height, the algorithm retrieves the number concentration and vertical profiles of liquid water content and particle effective radius. A novel aspect of the retrieval is that it depends upon an estimated particle median radius vertical profile that is derived from a statistical model that relates size to variations in particle vertical velocity; the model posits that the median particle radius is proportional to the fourth root of the particle velocity variance if the radii of particles in a parcel of zero vertical velocity is neglected. The performance of the retrieval is evaluated using data from two stratus case study days 1.5 and 8.0 h in temporal extent. Aircraft in situ microphysical measurements were available on one of the two days and the retrieved number concentrations and effective radii are consistent with them. The retrieved liquid water content and effective radius increase with height for both stratus cases, which agree with earlier studies. Error analyses suggest that the error in the liquid water content vanishes and the magnitudes of the fractional error in the effective radius and shortwave extinction coefficient computed from retrieved cloud particle size distributions are half of the magnitudes of the fractional error in the estimated cloud particle median radius if the fractional error in the median radius is constant with height.

An adaptive pathline-based particle tracking algorithm for the Eulerian–Lagrangian method

The accuracy in determining the Lagrangian concentration in the Eulerian–Lagrangian method depends on both the particle tracking algorithm and concentration interpolation. In most existing particle tracking algorithms, accurate tracking cannot be achieved, particularly in a complicated unsteady flow. Also mechanisms for error estimation and accuracy control are not available. A new algorithm is developed by refining the process of particle tracking, making use of a series of available travel time increments (ATTIs). The ATTIs are selected on the basis of tracking accuracy and efficiency. These are controlled by practical indices related to the rate of particle velocity variation (magnitude and direction). The particle velocity is determined by bilinear interpolation in space and time. The proposed algorithm combines an inter-element refinement, consistent with the piecewise interpolation of velocity, and an in-element pathline-based refinement. No mesh refinement is needed. Numerical simulations have been used to demonstrate the accuracy of the proposed algorithm. A comparison between the results obtained by using the proposed algorithm and by some existing techniques shows that the new algorithm can provide an accurate and efficient particle tracking, especially in a complicated unsteady heterogeneous flow.

Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations

A linear stability analysis is performed for the homogeneous state of a monodisperse gas-fluidized bed of spherical particles undergoing hydrodynamic interactions and solid-body collisions at small particle Reynolds number and finite Stokes number. A prerequisite for the stability analysis is the determination of the particle velocity variance which controls the particle-phase pressure. In the absence of an imposed shear, this velocity variance arises solely due to the hydrodynamic interactions among the particles. Since the uniform state of these suspensions is unstable over a wide range of values of particle volume fraction φ and Stokes number St, full dynamic simulations cannot be used in general to characterize the properties of the homogeneous state. Instead, we use an asymptotic analysis for large Stokes numbers together with numerical simulations of the hydrodynamic interactions among particles with specified velocities to determine the hydrodynamic sources and sinks of particle-phase energy. In this limit, the velocity distribution to leading order is Maxwellian and therefore standard kinetic theories for granular/hard-sphere molecular systems can be used to predict the particle-phase pressure and rheology of the bed once the velocity variance of the particles is determined. The analysis is then extended to moderately large Stokes numbers for which the anisotropy of the velocity distribution is considerable by using a kinetic theory which combines the theoretical analysis of Koch (1990) for dilute suspensions (φ [Lt ] 1) with numerical simulation results for non-dilute suspensions at large Stokes numbers. A linear stability analysis of the resulting equations of motion provides the first a priori predictions of the marginal stability limits for the homogeneous state of a gas-fluidized bed. Dynamical simulations following the detailed motions of the particles in small periodic unit cells confirm the theoretical predictions for the particle velocity variance. Simulations using larger unit cells exhibit an inhomogeneous structure consistent with the predicted instability of the homogeneous gas–solid suspension.

The Vavilov–Cherenkov radiation arising at deceleration of heavy ions in a transparent medium

Abstract Some results of the Vavilov–Cherenkov radiation arising at a nonuniform motion of a charged particle in a radiator are presented. Considerable broadening of the width of VChR ring in the case of the broader radiator compared to the thinner one is observed. The particle velocity variation in the radiator due to large energy losses of heavy ions is the only explanation of this effect.

Particle dispersion in forced isotropic low-Mach-number turbulence

Dispersion of solid particles in forced isotropic low-Mach-number turbulent flows s studied. The carrier phase is considered in the Eulerian frame and is simulated by direct numerical simulation (DNS) whereas the particles are treated in a Lagrangian context. The formulation includes the effects of the two-way coupling on the carrier phase. The results verify previous observations for velocity field in similar studies in incompressible flows while providing new insights into the modifications of the thermodynamic fields. It is found that the ratio of the root mean square (rms) Mach number to the mean Mach number is nearly constant (∼0.41) for all of the cases. A peak value is observed in the variation of the particle velocity variance (normalized with the fluid velocity variance) with the mass loading ratio. The polytropic coefficient decreases linearly by the increase of the mass loading ratio, and nonlinearly by the decrease of the particle time constant. © 1999 Elsevier Science Ltd. All rights reserved.

Simple shear flows of dilute gas–solid suspensions

Kinetic theory and numerical simulations are used to explore the dynamics of a dilute gas–solid suspension subject to simple shear flow. The particles experience a Stokes drag force and undergo solid-body interparticle collisions. Two qualitatively different steady-state behaviours are possible: an ignited state, in which the variance of the particle velocity is very large; and a quenched state, in which most of the particles follow the local fluid velocity. Theoretical results for the ignited state are obtained by perturbing from a Maxwell distribution, while predictions for the quenched state result from consideration of the collision of particles that initially move with the fluid. A composite theory, which includes effects of collisions driven by both the mean shear and the velocity fluctuations, predicts the existence of multiple steady states. Dynamic simulations and calculations using the direct-simulation Monte Carlo method confirm the result that, for certain volume fractions and shear rates, either the quenched or ignited state can be achieved depending on the initial velocity variance.Simulations are also performed for particles experiencing a nonlinear drag force. Both the theory of rapid granular flow, which neglects drag, and our theory for the ignited state with linear drag predict that the particle velocity variance can grow without bound as ϕ → 0, where ϕ is the volume fraction. The nonlinear drag force eliminates the divergence and leads to a particle velocity variance that will always decrease with decreasing volume fraction in the limit ϕ → 0.

Significance of relative velocity in the estimation of drag force of a tethered spherical float

In the present study, a tethered spherical float undergoing oscillatory motion in regular waves is analysed. Float velocity is computed through dynamical equation of motion and particle velocity using linear wave theory. The results show that variation of particle velocity with respect to wave period, wave height or water depth is small compared to the variation of float velocity with respect to the same parameters. The results further indicate that the difference between float velocity and particle velocity is considerable and, in such cases, the relative velocity instead of the particle velocity has to be considered for drag force or drag power estimation. However, it is suggested that float velocity must be higher than the particle velocity in order to use relative velocity in drag force or drag power estimation.

The effect of a mean fluid velocity gradient on the streamwise velocity variance of a particle suspended in a turbulent flow

The effect of a mean fluid velocity gradient on the motion of a small solid particle suspended in a turbulent gas is analyzed using Fourier transform techniques. The presence of a mean fluid velocity gradient is shown to elevate the streamwise particle velocity variance above the level predicted without such gradients; the particle velocity variance in the direction normal to the flow is shown to be only indirectly affected by the existence of fluid velocity gradients. When the particle Stokes number is small, the streamwise particle velocity variance is elevated above the level predicted in flows without mean velocity gradients at a rate which is linearly proportional to both the particle Stokes number, α, and the ratio of the streamwise velocity gradient to the characteristic frequency of the energy-containing eddies in the turbulent field, G/ω e , For particles with large Stokes numbers, the dominant mechanism by which particle streamwise velocity fluctuations are generated is through random interaction between the particle path and the mean fluid velocity gradient.

Heat transfer past particles entrained in an oscillating flow with and without a steady velocity

In order to investigate the heat transfer past particles entrained in an oscillating flow with and without a steady velocity, the two-dimensional, unsteady conservation equations of mass, momentum and energy for laminar flow in the gas phase are solved numerically in spherical coordinates. The particle momentum equation is also solved simultaneously with the gas phase equations in order to consider the effect of the particle entrainment on the heat transfer past particles. The numerical solution gives the particle velocity variation as well as the gas phase velocity and temperature distribution as a function of time. The local and space-averaged Nusselt number with particle entrainment is compared with that without particle entrainment. In the case of an oscillating flow with a steady velocity, the values of the space-averaged Nusselt number with particle entrainment are lower than those without particle entrainment at frequencies of 50 and 2000 Hz, since the moving particle is entrained in the steady velocity. In the case of an oscillating flow without a steady velocity, the space-averaged Nusselt number with entrainment at a frequency of 50 Hz is slightly lower than that without particle entrainment, with a phase lag. At 2000 Hz, the space-averaged Nusselt number with and without particle entrainment is almost the same, due to very small particle entrainment.

Effects of particle entrainment on heat transfer past particles in an oscillating flow

In order to investigate the effect of the particle entrainment on the heat transfer past paricles entrained in an oscillating flow with and without a steady velcoity, the two dimensional, unsteady, laminar conservation equations for mass, momentum and energy transport in the gas phase are solved numerically in spherical coordinates. The particle momentum equation is also solved simultaneously with the gas phase equations. The numerical solution gives the particle velocity variation as well as the gas phase velocity and temperature distribution as a function of time. The local and space-averaged Nusseit number with particle entrainment is compared with that without particle entrainment. In the case of an oscillating flow with a steady velocity, the values of the space-averaged Nusselt number with particle entrainment are lower than those without particle entrainment at frequencies of 50 and 2000 Hz since the moving particle is entrained in the steady velocity. In the case of an oscillating flow without a steady velocity, the space-averaged Nusselt number with entrainment at a frequency of 50 Hz is slightly lower than that without particle entrainment, with a phase lag. At 2000 Hz, the space-averaged Nusselt number with and without particle entrainment is almost the same, due to very small particle entrainment.

Un modèle de Bremsstrahlung couplant une trajectoire classique et un champ quantifié

A charged particle velocity variation induces a displacement of the equilibrium point of the electromagnetic field oscillators. Projecting the displaced initial wave function on the oscillators eigenstates we get a straightforward calculation of various multiphotonic Bremsstrahlung effects. The model is realistic only if the velocity change occurs in a time small versus the oscillators periods. Our results which are in substantial agreement with previous calculations may help to clarify a few points

Theoretical Analysis of a Technique for the Characterization of Myocardium Contraction Based Upon Temporal Correlation of Ultrasonic Echoes

The temporal correlation properties of ultrasonic echoes from contracting myocardium are investigated theoretically. Myocar- dium is modeled as a dense suspension of moving particles, with time- varying scattering amplitudes. Single scattering is assumed. Echoes from different particles are added coherently. The variance of particle velocity is proposed as an indicator of contractile performance. It is shown how this parameter may be extracted from the average corre- lation of pairs of echoes arising from separate ultrasound pulses. An experiment is performed in which a manufactured target with known motion characteristics is interrogated using a commercial medical ul- trasound scanner. The experimental results are found to be in good agreement with theory. Finally, practical considerations for perform- ing and interpreting these measurements in human myocardium are discussed. EVERAL INVESTIGATIONS have demonstrated that it may be possible to evaluate cardiac contractile per- formance accurately with ultrasound. One technique in- volves the measurement of the frequency average of the intensity of ultrasonic echoes emanating from myocar- dium. Echo intensity has been found to vary throughout the cardiac cycle in normal canine myocardium, with the maximum level occurring at end-diastole and the mini- mum at end-systole ( l), (2). In addition, the magnitude of this effect has a regional dependence throughout the heart, with areas of greater contractile activity exhibiting greater amplitudes of variation (3). The extent of the cyclic variation of echo intensity has also been observed to drop significantly in canine myocardium making a tran- sition from normal to ischemic 141. Thus the magnitude of cyclic variation may be interpreted as a measure of contractile performance. A second technique entails quantitative analysis of video images of the heart produced by ultrasound scan-

The determination of the instantaneous velocity of axonally transported organelles from filmed records of their motion.

A computational procedure is described for obtaining reproducible, low noise estimates of the instantaneous velocity of axonally transported organelles. Axonally transported organelles were detected in myelinated nerve fibers from Xenopus laevis by dark-field microscopy. The motion of the organelles was recorded on motion picture film at 3 frames/s, and the position of organelles travelling in the retrograde direction was obtained as a pair of x (axial) and y (transverse) coordinates at each 0.33-s interval. THe trend in organelle movement with time was calculated for each of the series of x and y coordinates by linear regression. This trend was removed from the measurements of x and y to yield sets of trend-free displacements. The trend yielded a measure of the mean velocity of the organelle in each of the two orthogonal directions. Power spectra of the deviations in x and y about the trend were calculated. For 133 particles studied, 99% of the power in the trend-free deviations occurred at frequencies below 0.3 Hz. The peak power in the x and y deviations occurred at a frequency of 0.1 Hz or less. Positional deviations about the trend were treated with a discrete 21-term differentiating filter that attenuated frequencies above 0.3 Hz. Instantaneous velocities for the organelles were obtained by adding the result of the band-limited differentiation to the appropriate estimates of mean velocity. The 21-term method was compared with a commonly used 2-term approximation to a differentiator and was shown to produce velocity estimates with about one order of magnitude less error. Estimates of organelle velocity obtained with the 21-term method indicate that saltatory particle motion may be viewed either as a smooth variation of particle velocity with respect to time or as an irregular, or discontinuous, variation of velocity with respect to particle position.

Variability and temperature dependence of the velocity of retrograde particle transport in myelinated axons.

The velocity of the retrograde transport of optically detectable particles was studied in isolated myelinated axons from Xenopus laevis at room temperature and with varying temperature. At room temperature (22–23.1 °C) the mean particle velocity was significantly different in some axons of the same animal. Results pooled from a number of axons did not indicate any significant difference in the average particle velocity in different animals. At room temperature, even though the mean particle velocity might differ between axons, the coefficient of variation of particle velocity in separate fibers tended to remain constant.The temperature dependence of mean particle velocity (V) could be adequately described by the relationship V = 0.26 exp 0.073T – 0.33, where V is in micrometres per second and T is degrees Celsius. Throughout the temperature range at which transport took place (approximately 5–35 °C) the coefficient of variation of particle velocity remained approximately constant at 0.40. All particles ceased their motion abruptly, and to some extent reversibly, at 37 °C. On morphological evidence, none of the effects of temperature appeared to be related to microtubule depolymerization.The results indicate that retrogradely transported particles with a wide range of velocities respond homogeneously to temperature changes. This supports the view that a common mechanism may underlie the motion of all the particles. No evidence was obtained that the differences between axons at room temperature could be attributed to the presence in separate axons of dissimilar proportions of faster and slower particles. Nor was the velocity–temperature characteristic in the region of room temperature sufficiently steep to explain the differences between axons. It is suggested that axons may differ in general mechanical or chemical properties so that the motion of all particles is affected uniformly.

Finite-amplitude behavior of N-shaped pulses from sparks

This paper is a review of experiments done in our laboratory on airborne N waves generated by electric sparks. The purpose of the experiments has been to investigate the effects of finite amplitude on a variety of classical wave phenomena. The N waves used have duration 10-70 μsec, amplitude 0.1 – 100 mbar, and risetime frequently less than 1 μsec. Experiments have been done on simple propagation in an open medium; refraction and diffraction by an acoustic lens (a gas-filled soap bubble); diffraction by a circular aperture, by a disk, and by a slit; focusing by a spherical mirror; and propagation in waveguides (parallel plates and circular tube). All nonlinear effects observed may be traced to modification of the propagation speed by the acoustic field itself. The modification causes elongation and extra decay of simple propagating N waves, unusual interference effects in diffraction, and self-refraction. Self-refraction, which is bending of rays due to a variation of particle velocity (and therefore propagation speed) from ray to ray, sometimes prevents converging rays from actually focusing. [Work supported by ONR, AFOSR, and NASA.]

Particle circulation in a spouted bed

Based on experimental data, a discussion is presented on particle circulation in a spouted bed produced by introducing air in a 100 mm diameter semi-circular, conical-bottom column, provided with a transparent frontal wall. A high speed camera was used to determine particle movement in the bed. Characteristic pictures show the trajectories of the particles in the spout and in the annulus. Comments are presented on the axial and radial particle velocity variation in the two zones of the spouted bed. A relation between particle velocity in the annulus, at a given level, and the minimum spouting velocity is presented. It is thought that this relation may constitute a reasonable basis for an equation of more general use. The experimental data regarding the average bulk velocity of particles in the annulus point to a value equal to that of particles located at a distance of 0.7 – 0.8 R from the axis of the column. This is in contradiction to previous work, where the average bulk velocity of the particles in the annulus was taken equal to that of the particles moving along and in contact with the wall.

Interferometric measurement of shock-induced internal particle velocity and spatial variations of particle velocity

Methods of applying laser interferometry to measure particle velocity history at the interface between a shocked specimen and a transparent window material are discussed. Particular emphasis is given to diffusely reflecting interface surfaces, to shock-induced light polarization shifts which can occur in the window material, and to a transient loss of fringe contrast which occurs whenever the reflecting surface velocity is spattially nonuniform. It is shown that the loss of finge contrast can be used to provide time-resolved measurements of the spatial variations in particle velocity.