DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured.The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

Particle dynamics in dense shear granular flow

The particle dynamics in an annular shear granular flow is studied using the discrete element method, and the influences of packing fraction, shear rate and friction coefficient are analyzed. We demonstrate the existence of a critical packing fraction exists in the shear granular flow. When the packing fraction is lower than this critical value, the mean tangential velocity profile exhibits a rate-independent feature. However, when the packing fraction exceeds this critical value, the tangential velocity profile becomes rate-dependent and varies gradually from linear to nonlinear with increasing shear rate. Furthermore, we find a continuous transition from the unjammed state to the jammed state in a shear granular flow as the packing fraction increases. In this transforming process, the force distribution varies distinctly and the contact force network also exhibits different features.     

Particle size and boundary geometry effects on the bulk friction coefficient of sheared granular materials in the inertial regime

Glass beads of varying diameters (d=2,3,4$d=2,3,4$, and 5 mm) are used to measure the ratio of shear-to-normal stress, or bulk friction coefficient, generated inside an annular shear cell at high shearing rates. The effects of the particle size, the solids concentration, and the shear rate are explored. It is found that (1) for a given particle size, the magnitude of the bulk friction coefficient decreases with increasing solids concentration, (2) for a given solids concentration, the bulk friction coefficient decreases with increasing particle size, and (3) the bulk friction coefficient is independent of the shear rate except for cases with low solids concentration, where it decreases with increasing shear rate. The boundary geometry is found to affect bulk friction only for dilute (low solids concentration) flows involving small particles.     

Hydrodynamic mixing in a granular bed with irregular packing

In investigating longitudinal [1–4] and transverse [5] mixing in a granular bed described by a cellular model it has so far been assumed that all the cells are identical, while the parameters of the distribution function of the residence time in the individual cell (henceforth called the microdistribution) are strictly fixed. In an actual granular bed with irregular packing the identical cell condition is obviously not satisfied and the microdistribution parameters may be regarded as random quantities. This paper is concerned with an investigation of the effect of the spread of microdistribution parameters on the characteristics of the process of longitudinal and transverse transport of a neutral fluid in a granular bed.While retaining the general structure of the cellular model [5], we assume that the gas or liquid passing through the bed flows from the cells on one horizontal level into the cells on the next level downstream, its motion in the transverse direction being random. Obviously, a particle of the fluid passing through the granular bed can then occupy one cell on each horizontal level. Dropping the identical cell condition, we assume that the bed is homogeneous and that the parameters of the cells successively occupied by a fluid particle are statistically independent. This assumption means that cells with different values of the parameters have been well mixed, so that inside the bed there are no fluctuations significantly exceeding the cell dimension in extent.The authors thank V. G. Levich for his interest and helpful advice.     

Particle collisions in a turbulent flow

An equation for the two-point probability density function of the two-particle the coordinate and velocity distribution is obtained. A closed system of equations for the first and second two-point moments of the velocity fluctuations of a pair of particles with allowance for the turbulent flow inhomogeneity is given. Boundary conditions for the equations of the particle concentration and the intensity of the relative random velocity during particle collision are obtained. A unified formula describing the interparticle collision process as a result of turbulent motion and the average relative particle velocity slip is obtained for the kernel of the coagulation equation. The effect of the average velocity slip of the particles and the carrier phase on the parameters of motion of the dispersed admixture and its coagulation is investigated on the basis of a two-point two-time velocity fluctuation autocorrelation function with two time and space scales representing the energy-bearing and small-scale motion of the fluid phase.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–116, March–April, 1996.     

Analysis of energy transfers of a sheared flow generated by wall injection

 We propose in this work to characterize the unsteady behavior of a flow generated by wall injection and encountering an obstacle. This sutdy concerns the prediction of the stability of segmented solid propellant rocket motors. The simulation of such a system is studied in cold flow, which makes it possible to analyze the basic phenomena and the energy transfer mechanisms of the flow. The results obtained allow the identification of the vortex structures by visualization inside a shear layer created at the top of an obstacle. The analysis of the pressure field shows that the dynamic parameters (mass flow rate or flow velocity) generate a phenomenon of selective excitation and of longitudinal acoustic modes amplification, which is accompanied by an energy transfer between modes. Received: 30 October 1997 / Accepted: 8 June 1998     

Particle suspension in a simple shear flow

A hydrodynamic model describing the particle distribution over the cross-section of a finely dispersed flow is proposed. The model is constructed on the basis of notions concerning the diffusion of particles induced by their random displacements in the process of relative motion of neighboring layers at constant shear velocity. It is shown that the suspension capacity of the flow is large for small particles due to thermal fluctuations and for relatively large particles due to shear-induced particle pulsations. There are critical particle sizes for which the particles are suspended and transported by the flow less effectively than larger or smaller particles.Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 112–121, January–February, 1995.     

Particle deposition from a turbulent flow

The diffusion equations and boundary condition for particle deposition from a turbulent flow are obtained on the basis of the kinetic equation for the probability density of the particle distribution. This approach makes it possible to calculate the deposition fairly simply without introducing additional empirical information relating to the particles (empirical constants are needed only for calculating the characteristics of the turbulent carrier flow). Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 96–104, September–October, 1988.     

Particle and bubble dynamics in a creeping flow

Dynamics of a solid particle and non-deformable gaseous bubble in viscous fluid are studied analytically and numerically within the framework of creeping flow regime (flow at vanishingly small Reynolds numbers). Equations of motion for the particle and bubble include the consideration of the buoyancy force, Stokes drag force and memory-integral drag force. Exact analytical solutions are obtained and categorised in terms of inclusion (particle or bubble) density with respect to the density of a surrounding fluid. Through the analytical and numerical solutions, the dynamics of solid particle and air bubble in water have been found to behave differently especially at the early stages of motion, whereas some qualitative similarities exist in the long-term asymptotic.     

Particle dispersion in a single-sided backward-facing step flow

The paper describes the particle dispersion in a single-sided backward-facing step flow. Particles of well-known sizes in the diameter range from 1 to 70 μm were suspended in an air flow and the particle motion over a step was measured by mean of a laser-Doppler anemometer. Thus, the local and integral flow quantities, i.e. the mean and turbulent velocity data could be measured precisely. In the experiments, monodispersed particle size distributions were used to exclude particle size related information ambiguity, known as triggering effects or size bias. The results of this study show qualitatively and quantitatively the difference in time-averaged particle dynamics for selected particle sizes in a backward-facing step flow. The experiments show, for different sizes, the changes in the particle velocity field in comparison with the velocity field of the continuous phase deduced from the 1 μm particles, and also imply the strong influences which different particle sizes have on flow data evaluation when size effects are not taken into account with particle-related optical measuring techniques.     

Particle response in a planar sudden expansion flow

Particle velocity and concentration statistics were measured in a vertically downward planar sudden expansion flow for large-eddy particle Stokes numbers (τ_pU_o/5H) ranging from 0.5 to 7.4. Particles with Stokes numbers greater than 3 did not enter the recirculation zone, exhibited substantial attenuation of cross-stream velocity fluctuations, and had large streamwise velocity fluctuations in regions of strong velocity gradient. The smallest particles filled the recirculation zone and showed strong response to the large eddies in the flow. Phase-locked particle concentration measurements showed that these particles were centrifuged away from vortex cores and concentrated between vortices. Intermediate-size particles with Stokes numbers of 1.4 were injected intermittently into the recirculation zone as tongues of particles moving down between vortices. Particle Reynolds number was found to have negligible effect on the particle velocity statistics.     

Particle motions in sheared suspensions XXII: Interactions of rigid spheres (experimental)

Summary The behaviour of rigid spheres suspended in viscous liquids undergoing laminar shear flow was compared experimentally with the approximate theory developed earlier. Good agreement was obtained for a sphere near a wall and for equatorial interactions between two spheres of both equal and unequal diameters. In the region close to but not touching the wall, the theory byGoldman et al. accurately described the motion of a sphere. The prediction that a sphere touching the wall should stick to it could not be confirmed. A viewing device, designed to study motions in two planes simultaneously was used to make several interesting observations on permanent and separating doublet. Some similarities between collisions in the equatorial plane and two-body interactions of vertically oriented rigid circular cylinders were noted. The asymmetry and reversibility of triple collisions as well as the ease of formation of permanent doublets in flowing suspensions were established.

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Zusammenfassung Das Verhalten von starren, in viskosen Flüssigkeiten suspendierten Teilchen unter dem Einfluß von laminarem Scherfluß wurde experimentell mit der früher entwickelten, genäherten Theorie verglichen. Gute Übereinstimmung wurde erhalten für eine Kugel in Wandnähe und für äquatoriale Einflüsse zwischen zwei Kugeln von entweder gleichem oder verschiedenem Durchmesser. Die Theorie vonGoldmann et al. gab eine genaue Beschreibung der Bewegung einer Kugel in Wandnähe, aber ohne Wandberührung. Die Voraussage, daß eine Kugel an einer berührenden Wand kleben würde, konnte nicht bestätigt werden. Eine Beobachtungs-Einrichtung, die für das Studium der gleichzeitigen Bewegung in zwei Ebenen konstruiert war, wurde für verschiedene interessante Beobachtungen an permanenten und an sich trennenden Dubletts benutzt. Einige Änlichkeiten zwischen Zusammenstößen in der Äquatorial-Ebene und Zweikörperbeinflussungen von vertikal orientierten, starren kreisförmigen Zylindern wurde festgestellt. Die Asymmetrie und Reversibilität von dreifachen Stößen wie auch die leichte Bildung von permanenten Dubletts wurde im Fluß von Suspensionen festgestellt.

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This work was also supported by the National Heart Institute of the United States Public Health Service (Grant HE-05911).     

Secondary flow patterns and mixing in laminar pulsating flow through a curved pipe

Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r ₀/r _c  = 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced. To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe. Experiments are carried out for the Reynolds numbers range 420 ≤ Re_st ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U _max,osc/U _m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters 8.37 < (α = r ₀(ω/ν)^0.5) < 24.5, where α² is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing. The effects of each parameter (Re_st, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ _P |/|ζ _S |) and dimensionless transverse strain rates (|ε _P |/|ε _S |) during a complete oscillation period.     

Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow

Large-scale model testing of a tensioned steel riser in well-defined sheared current was performed at Hanøytangen outside Bergen, Norway in 1997. The length of the model was 90 m and the diameter was 3 cm. The aim of the present work is to look into this information and try to improve the understanding of vortex-induced vibrations (VIV) for cases with very high order of responding modes, and in particular to study if and under which circumstances the riser motions would be single-mode or multi-mode. The measurement system consisted of 29 biaxial gauges for bending moment. The signals are processed to yield curvature and displacement and further to identify modes of vibration. A modal approach is used successfully employing a combination of signal filtering and least-squares fitting of precalculated mode-shapes. As a part of the modal analysis, it is demonstrated that the equally spaced instrumentation limited the maximum mode number to be extracted to be equal to the number of instrumentation locations. This imposed a constraint on the analysis of in-line (IL) vibration, which occurs at higher frequencies and involves higher modes than cross-flow (CF). The analysis has shown that in general the riser response was irregular (i.e. broad-banded) and that the degree of irregularity increases with the flow speed. In some tests distinct spectral peaks could be seen, corresponding to a dominating mode. No occurrences of single-mode (lock-in) were seen. The IL response is more broad-banded than the CF response and contains higher frequencies. The average value of the displacement r.m.s over the length of the riser is computed to indicate the magnitude of VIV motion during one test. In the CF direction the average displacement is typically 1/4 of the diameter, almost independent of the flow speed. For the IL direction the values are in the range 0.05–0.08 of the diameter. The peak frequency taken from the spectra of the CF displacement at riser midpoint show approximately to be equal to the Strouhal frequency. The peak frequency in IL direction was typically twice the Strouhal frequency.