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1
Chen, Rongqian, Yi Liu, and Deming Nie. "Computer Simulation of Three Particles Sedimentation in a Narrow Channel." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/1259840.
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The settling of three particles in a narrow channel is simulated via the lattice Boltzmann direct-forcing/fictitious domain (LB-DF/FD) method for the Reynolds number ranging from 5 to 200. The effects of the wall and the Reynolds number are studied. It is interesting to find that at certain Reynolds numbers the left (right) particle is settling at 0.175 (0.825) of the channel width irrespective of its initial position or the channel width. Moreover, numerical results have shown that the lateral particles lead at small Reynolds numbers, while the central particle leads at large Reynolds numbers due to the combined effects of particle-particle and particle-wall interactions. The central particle will leave the lateral ones behind when the Reynolds number is large enough. Finally the effect of the Reynolds number on the trajectory of the lateral particles is presented.
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Mao, Wenbin, and Alexander Alexeev. "Motion of spheroid particles in shear flow with inertia." Journal of Fluid Mechanics 749 (May 14, 2014): 145–66. http://dx.doi.org/10.1017/jfm.2014.224.
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AbstractIn this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.
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DANIEL, W. BRENT, ROBERT E. ECKE, G. SUBRAMANIAN, and DONALD L. KOCH. "Clusters of sedimenting high-Reynolds-number particles." Journal of Fluid Mechanics 625 (April 14, 2009): 371–85. http://dx.doi.org/10.1017/s002211200900620x.
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We report experiments wherein groups of particles were allowed to sediment in an otherwise quiescent fluid contained in a large tank. The Reynolds number of the particles, defined as Re = aU/ν, ranged from 93 to 425; here, a is the radius of the spherical particle, U its settling velocity and ν the kinematic viscosity of the fluid. The characteristic size of a cluster, in a plane transverse to gravity, was measured by a ‘cluster variance’(〈r2t〉); the latter is defined as the mean square of the transverse coordinates of all constituent particles, averaged over a series of runs. The cluster variance, when plotted as a function of time, exhibited two regimes. There was a quadratic growth in the variance at short times(〈r2t〉 ∝ t2), while for long times, the cluster variance exhibited a slower sublinear growth with 〈r2t〉 ∝ t0.67. A theory, based on isotropic repulsive hydrodynamic interactions between particles, predicts the cluster variance to grow as t2/3 in the limit of long times. The theoretical framework was originally proposed to describe the long-time self-similar evolution of dilute clusters in the limit Re ≪ 1 Subramanian & Koch (J. Fluid Mech., vol. 603, 2008, p. 63), when the probability of wake-mediated interactions between particles remains asymptotically small; the latter requirement is satisfied for homogeneous spherical clusters larger than a critical radius, and is evidently satisfied for planar clusters oriented transversely to gravity. The isotropy of the interactions therefore stems from the isotropy, at large distances, of the disturbance velocity field produced by a single sedimenting particle outside its wake(which contains the compensating inflow to satisfy mass conservation). Herein, the theory is extended to large Re using an empirical correlation for the drag on a sedimenting particle. This allows one to predict, as a function of Re, the numerical prefactors in the expressions for the cluster variance of both spherical and planar clusters; the predictions for the growth exponent remain unchanged. The agreement between the theoretical and experimental growth exponents supports the hypothesis of a self-similar expansion at long times. The prefactor determined from the experimental observations is found to lie between the theoretical predictions for planar and spherical clusters.
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Nie, Deming, Jianzhong Lin, and Mengjiao Zheng. "Direct Numerical Simulation of Multiple Particles Sedimentation at an Intermediate Reynolds Number." Communications in Computational Physics 16, no. 3 (September 2014): 675–98. http://dx.doi.org/10.4208/cicp.270513.130314a.
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AbstractIn this work the previously developed Lattice Boltzmann-Direct Forcing/ Fictitious Domain (LB-DF/FD) method is adopted to simulate the sedimentation of eight circular particles under gravity at an intermediate Reynolds number of about 248. The particle clustering and the resulting Drafting-Kissing-Tumbling (DKT) motion which takes place for the first time are explored. The effects of initial particle-particle gap on the DKT motion are found significant. In addition, the trajectories of particles are presented under different initial particle-particle gaps, which display totally three kinds of falling patterns provided that no DKT motion takes place, i.e. the concave-down shape, the shape of letter “M” and “in-line” shape. Furthermore, the lateral and vertical hydrodynamic forces on the particles are investigated. It has been found that the value of Strouhal number for all particles is the same which is about 0.157 when initial particle-particle gap is relatively large. The wall effects on falling patterns and particle expansions are examined in the final.
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Mei, Renwei, and Ronald J. Adrian. "Effect of Reynolds Number on Isotropic Turbulent Dispersion." Journal of Fluids Engineering 117, no. 3 (September 1, 1995): 402–9. http://dx.doi.org/10.1115/1.2817276.
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The influence of the spatio-temporal structure of isotropic turbulence on the dispersion of fluid and particles with inertia is investigated. The spatial structure is represented by an extended von Ka´rma´n energy spectrum model which includes an inertial sub-range and allows evaluation of the effect of the turbulence Reynolds number, Reλ. Dispersion of fluid is analyzed using four different models for the Eulerian temporal auto-correlation function D(τ). The fluid diffusivity, normalized by the integral length scale L11 and the root-mean-square turbulent velocity u0, depends on Reλ. The parameter cE = T0u0/L11, in which T0 is the Eulerian integral time scale, has commonly been assumed to be constant. It is shown that cE strongly affects the value of the fluid diffusivity. The dispersion of a particle with finite inertia and finite settling velocity is analyzed for a large range of a particle inertia and settling velocity. Particle turbulence intensity and diffusivity are influenced strongly by turbulence structure.
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Tu, Chengxu, and Jian Zhang. "Nanoparticle-laden gas flow around a circular cylinder at high Reynolds number." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 8 (October 28, 2014): 1782–94. http://dx.doi.org/10.1108/hff-03-2013-0101.
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Purpose – Experiments to investigate the characteristic distribution of nanoparticle-laden gas flow around a circular cylinder were performed with a fast mobility particle spectrometer. The paper aims to discuss these issues. Design/methodology/approach – The fast mobility particle sizer spectrometer is used to measure quasi-instantaneous particle number density. The acquired particle number density, total concentration, and geometric mean diameter at free stream and in the wake were used to discuss the particle characteristic distribution. The time-averaged velocity field detected by particle imaging velocimetry was used to investigate the effect of carried phase on nanoparticles distribution. Findings – Results show that the total particle concentration in the free stream is larger than that in the wake. However, the geometric mean diameter of particle in the free stream is smaller than that in the wake for different Re. The total particle concentration and geometric mean diameter in the free stream and the wake both change in the same way, but with an obvious lag which increases with Re. Despite particle deposition, the number density of particles with electrical-mobility-equivalent diameters in the range from 220.7 to 523.3 nm in the wake is still higher than that in the free stream. Originality/value – Though the particles-laden gas flow around a circular cylinder had been studied experimentally and numerically before, where particles are larger than one micrometer, investigators paid little attention on the nanoparticles-laden gas flow where particles are smaller than one micrometer, especially at high Reynolds number, because numerical methods so far cannot deal these problems completely and satisfactorily. However, this issue is widely existing in nature and engineering application, such as superfine dust or microorganism captured by a circular cylinder model.
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Almerol, Jenny Lynn Ongue, and Marissa Pastor Liponhay. "Clustering of fast gyrotactic particles in low-Reynolds-number flow." PLOS ONE 17, no. 4 (April 7, 2022): e0266611. http://dx.doi.org/10.1371/journal.pone.0266611.
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Systems of particles in turbulent flows exhibit clustering where particles form patches in certain regions of space. Previous studies have shown that motile particles accumulate inside the vortices and in downwelling regions, while light and heavy non-motile particles accumulate inside and outside the vortices, respectively. While strong clustering is generated in regions of high vorticity, clustering of motile particles is still observed in fluid flows where vortices are short-lived. In this study, we investigate the clustering of fast swimming particles in a low-Reynolds-number turbulent flow and characterize the probability distributions of particle speed and acceleration and their influence on particle clustering. We simulate gyrotactic swimming particles in a cubic system with homogeneous and isotropic turbulent flow. Here, the swimming velocity explored is relatively faster than what has been explored in other reports. The fluid flow is produced by conducting a direct numerical simulation of the Navier-Stokes equation. In contrast with the previous results, our results show that swimming particles can accumulate outside the vortices, and clustering is dictated by the swimming number and is invariant with the stability number. We have also found that highly clustered particles are sufficiently characterized by their acceleration, where the increase in the acceleration frequency distribution of the most clustered particles suggests a direct influence of acceleration on clustering. Furthermore, the acceleration of the most clustered particles resides in acceleration values where a cross-over in the acceleration PDFs are observed, an indicator that particle acceleration generates clustering. Our findings on motile particles clustering can be applied to understanding the behavior of faster natural or artificial swimmers.
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Heymsfield, Andrew, and Robert Wright. "Graupel and Hail Terminal Velocities: Does a “Supercritical” Reynolds Number Apply?" Journal of the Atmospheric Sciences 71, no. 9 (August 28, 2014): 3392–403. http://dx.doi.org/10.1175/jas-d-14-0034.1.
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Abstract This study characterizes the terminal velocities of heavily rimed ice crystals and aggregates, graupel, and hail using a combination of recent drag coefficient and particle bulk density observations. Based on a nondimensional Reynolds number (Re)–Best number (X) approach that applies to atmospheric temperatures and pressures where these particles develop and fall, the authors develop a relationship that spans a wide range of particle sizes. The Re–X relationship can be used to derive the terminal velocities of rimed particles for many applications. Earlier observations suggest that a “supercritical” Reynolds number is reached where the drag coefficient for large spherical ice—hail—drops precipitously and the terminal velocities increase rapidly. The authors draw on observations and model simulations for slightly roughened large ice particles that suggest that the critical Reynolds number is dampened and that the rapid increase in the terminal velocity of smooth spherical ice particles rarely occurs for natural hailstones.
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Wu, Zhenqun, Hui Jin, and Leijin Guo. "Investigation on the drag coefficient of supercritical water flow past sphere-particle at low reynolds numbers." Thermal Science 21, suppl. 1 (2017): 217–23. http://dx.doi.org/10.2298/tsci17s1217w.
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Supercritical water fluidized bed is novel reactor for the efficient gasification of coal to produce hydrogen. The Euler-Euler and Euler-Lagrange methods can be used to simulate the flow behaviors supercritical water fluidized bed. The accuracy of the simulated results with the two methods has a great dependence on the drag coefficient model, and there is little work focused on the study on particle?s drag force in supercritical water. In this work, the drag coefficients of supercritical water flow past a single particle and particle cluster. The simulated results show that the flow field and drag coefficient of single particle at supercritical condition have no difference to that at ambient conditions when the Reynolds number is same. For the two-particles model, a simplification of particle cluster, the drag coefficients of the two particles are identical at different conditions for the same Reynolds number. The variation characteristics with the Reynolds number and particles? positions are also same.
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Espinosa-Gayosso, Alexis, Marco Ghisalberti, Gregory N. Ivey, and Nicole L. Jones. "Particle capture and low-Reynolds-number flow around a circular cylinder." Journal of Fluid Mechanics 710 (September 7, 2012): 362–78. http://dx.doi.org/10.1017/jfm.2012.367.
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AbstractParticle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism in a range of environmental processes. In aquatic systems, typically characterized by low collector Reynolds numbers ($\mathit{Re}$), the rate of particle capture determines the efficiencies of a range of processes such as seagrass pollination, suspension feeding by corals and larval settlement. In this paper, we use direct numerical simulation (DNS) of a two-dimensional laminar flow to accurately quantify the rate of capture of low-inertia particles by a cylindrical collector for $\mathit{Re}\leq 47$ (i.e. a range where there is no vortex shedding). We investigate the dependence of both the capture rate and maximum capture angle on both the collector Reynolds number and the ratio of particle size to collector size. The inner asymptotic expansion of Skinner (Q. J. Mech. Appl. Maths, vol. 28, 1975, pp. 333–340) for flow around a cylinder is extended and shown to provide an excellent framework for the prediction of particle capture and flow close to the leading face of a cylinder up to $\mathit{Re}= 10$. Our results fill a gap between theory and experiment by providing, for the first time, predictive capability for particle capture by aquatic collectors in a wide (and relevant) Reynolds number and particle size range.
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LEU, TZONG-SHYNG, and CHING-YI PAI. "PARTICLE-FREE EXTRACTION BY USING MICROCHANNEL STRUCTURES." International Journal of Modern Physics: Conference Series 19 (January 2012): 237–41. http://dx.doi.org/10.1142/s201019451200880x.
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Modern separation methods of particles are usually prepared by large equipments. In this study, microfluidic chips with backward-facing-step (BFS) microchannel structures and centrifugal force are used to extract particle-free fluid from physical samples at the branch. Numerical simulation and experimental studies were performed to investigate the effects of inlet Reynolds number ( Re 0), as well as the particle-free fluid outlet Reynolds number ( Re 1), on the minimum radius of particles (R) that can be excluded from the particle-free fluid outlet channel. The fraction of the volumetric flow rate of particle-free extraction α (=extraction flow rate/inlet flow rate) was also obtained to evaluate the efficiency of particle-free extraction. Based on the numerical and experimental results, it is found that the design with 90° elbow inlet channel has a better performance than straight inlet channel. In this experiment, 1.0 μm radius of particles can be successfully separated from the fluid, and the volumetric fraction of the extraction flow rate was approximately 1.8% when inlet and outlet Reynolds numbers are 90 and 3.0 respectively.
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PATANKAR, N. A., T. KO, H. G. CHOI, and D. D. JOSEPH. "A correlation for the lift-off of many particles in plane Poiseuille flows of Newtonian fluids." Journal of Fluid Mechanics 445 (October 16, 2001): 55–76. http://dx.doi.org/10.1017/s0022112001005274.
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Choi & Joseph (2001) reported a two-dimensional numerical investigation of the lift-off of 300 circular particles in plane Poiseuille flows of Newtonian fluids. We perform similar simulations. Particles heavier than the fluid are initially placed in a closely packed ordered configuration at the bottom of a periodic channel. The fluid–particle mixture is driven by an external pressure gradient. The particles are suspended or fluidized by lift forces that balance the buoyant weight perpendicular to the flow. Pressure waves corresponding to the waves at the fluid–mixture interface are observed. During the initial transient, these waves grow, resulting in bed erosion. At sufficiently large shear Reynolds numbers the particles occupy the entire channel width during the transient. The particle bed eventually settles to an equilibrium height which increases as the shear Reynolds number is increased. Heavier particles are lifted to a smaller equilibrium height at the same Reynolds number. A correlation for the lift-off of many particles is obtained from the numerical data. The correlation is used to estimate the critical shear Reynolds number for lift-off of many particles. The critical shear Reynolds number for lift-off of a single particle is found to be greater than that for many particles. The procedures used here to obtain correlations from direct simulations in two dimensions and the type of correlations that emerge should generalize to three-dimensional simulations at present underway.
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Rostami, M., A. Ardeshir, G. Ahmadi, and P. J. Thomas. "On the effect of gravitational and hydrodynamic forces on particle motion in a quiescent fluid at high particle Reynolds numbers." Canadian Journal of Physics 86, no. 6 (June 1, 2008): 791–99. http://dx.doi.org/10.1139/p07-198.
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Trajectories of 5 and 10 mm metallic and plastic particles in a quiescent liquid during their sedimentation toward a plate were studied using experimental and numerical means, and the influence of gravity, drag, added mass, and history forces were evaluated. Variations of particle diameter and density allowed measurements at Reynolds numbers, based on the impact velocity, in the range of 1 000 to 13 000. A computer model was developed and the Lagrangian equation of particle motion was solved. The results showed that the combination of gravity, drag, and added mass forces are important for the simulation of the motion of small particles for the duration of their flight from the starting point to the wall impact, in the range of particle Reynolds numbers between 1000 and 5000. Comparison of the simulation results with the data showed that the predicted trajectories underestimated the experimental observations by about 1% to 4.3%. When the history force was included in the governing equation, however, excellent agreement between the measured and predicted particle trajectory was obtained. Experimental results for the motion of large particles showed oscillations in the time history of particle velocity when the particle Reynolds number was in the range of 3 000 to 13 000. Repeating the experiment, and averaging the data of a large number of experiments, yielded averaged curves for the particle velocity that did not show oscillatory values. In this case, good agreement between numerical and experimental data was observed. The study also shows that at high particle Reynolds numbers, the effect of the history force becomes negligibly small.PACS No.: 47.55kf
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VOTH, GREG A., A. LA PORTA, ALICE M. CRAWFORD, JIM ALEXANDER, and EBERHARD BODENSCHATZ. "Measurement of particle accelerations in fully developed turbulence." Journal of Fluid Mechanics 469 (October 15, 2002): 121–60. http://dx.doi.org/10.1017/s0022112002001842.
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We use silicon strip detectors (originally developed for the CLEO III high-energy particle physics experiment) to measure fluid particle trajectories in turbulence with temporal resolution of up to 70000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 [ges ] Rλ [ges ] 970. Particle trajectories exhibiting accelerations up to 16000 m s −2 (40 times the r.m.s. value) are routinely observed. The probability density function of the acceleration is found to have Reynolds-number-dependent stretched exponential tails. The moments of the acceleration distribution are calculated. The scaling of the acceleration component variance with the energy dissipation is found to be consistent with the results for low-Reynolds-number direct numerical simulations, and with the K41-based Heisenberg–Yaglom prediction for Rλ [ges ] 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at Rλ = 970. The coupling of the acceleration to the large-scale anisotropy is found to be large at low Reynolds number and to decrease as the Reynolds number increases, but to persist at all Reynolds numbers measured. The dependence of the acceleration variance on the size and density of the tracer particles is measured. The autocorrelation function of an acceleration component is measured, and is found to scale with the Kolmogorov time τη.
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HEWITT, G. F., and J. S. MARSHALL. "Particle focusing in a suspension flow through a corrugated tube." Journal of Fluid Mechanics 660 (July 21, 2010): 258–81. http://dx.doi.org/10.1017/s0022112010002697.
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A computational study is performed of the transport of a particulate suspension through a corrugated tube using a discrete-element method (DEM). The tube is axisymmetric with a radius that varies sinusoidally along the tube length, which, in the presence of a mean suspension flow, leads to periodic inward and outward acceleration of the advected particles. The oscillations in radial acceleration and straining rate lead to a net radial drift, with mean acceleration measuring about an order of magnitude smaller than the instantaneous radial acceleration, which over time focuses small particles within the tube. The foundations of particle focusing in this flow are examined analytically using lubrication theory, together with a low-Stokes-number approximation for the particle drift. This lubrication-theory solution provides the basic scaling for how the particle drift will vary with wave amplitude and wavelength. Computations are then performed using a finite-volume method for a fluid flow in the tube at higher Reynolds numbers over a range of amplitudes, wavelengths and Reynolds numbers, examining the effect of each of these variables on the averaged radial fluid acceleration. A DEM is used to simulate particle behaviour at finite Stokes numbers, and the results are compared to an asymptotic approximation valid for low Stokes numbers. At low tube Reynolds number (e.g. Re = 10), the drift velocity induced by the tube corrugations focuses the particles onto the tube centreline, in accordance with the low-Stokes-number approximation based on the axial-averaged fluid radial acceleration. At higher tube Reynolds numbers (e.g. Re = 100), the correlation between the particle radial oscillation and the fluid acceleration field leads the outermost particles to drift into a ring at a finite radius from the tube centre, with little net motion of the particles in the innermost part of the tube. At larger Stokes numbers, particles can be dispersed to the outer regions of the tube due to particle outward dispersion from the large instantaneous radial acceleration. The effects of eddy formation within the corrugation crests on particle focusing are also examined.
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Lin, Wenqian, Ruifang Shi, and Jianzhong Lin. "Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow." Applied Sciences 11, no. 3 (January 21, 2021): 962. http://dx.doi.org/10.3390/app11030962.
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Distribution and deposition of cylindrical nanoparticles in a turbulent pipe flow are investigated numerically. The equations of turbulent flow including the effect of particles are solved together with the mean equations of the particle number density and the probability density function for particle orientation including the combined effect of Brownian and turbulent diffusion. The results show that the distribution of the particle concentration on the cross-section becomes non-uniform along the flow direction, and the non-uniformity is reduced with the increases of the particle aspect ratio and Reynolds number. More and more particles will align with their major axis near to the flow direction, and this phenomenon becomes more obvious with increasing the particle aspect ratio and with decreasing the Reynolds number. The particles in the near-wall region are aligned with the flow direction obviously, and only a slight preferential orientation is observed in the vicinity of pipe’s center. The penetration efficiency of particle decreases with increasing the particle aspect ratio, Reynolds number and pipe length-to-diameter ratio. Finally, the relationship between the penetration efficiency of particle and related synthetic parameters is established based on the numerical data.
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McLaughlin, John B. "Inertial migration of a small sphere in linear shear flows." Journal of Fluid Mechanics 224 (March 1991): 261–74. http://dx.doi.org/10.1017/s0022112091001751.
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The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.
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Rubinstein, Gregory J., J. J. Derksen, and Sankaran Sundaresan. "Lattice Boltzmann simulations of low-Reynolds-number flow past fluidized spheres: effect of Stokes number on drag force." Journal of Fluid Mechanics 788 (January 8, 2016): 576–601. http://dx.doi.org/10.1017/jfm.2015.679.
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In a fluidized bed, the drag force acts to oppose the downward force of gravity on a particle, and thus provides the main mechanism for fluidization. Drag models that are employed in large-scale simulations of fluidized beds are typically based on either fixed-particle beds or the sedimentation of particles in liquids. In low-Reynolds-number ($Re$) systems, these two types of fluidized beds represent the limits of high Stokes number ($St$) and low $St$, respectively. In this work, the fluid–particle drag behaviour of these two regimes is bridged by investigating the effect of $St$ on the drag force in low-$Re$ systems. This study is conducted using fully resolved lattice Boltzmann simulations of a system composed of fluid and monodisperse spherical particles. In these simulations, the particles are free to translate and rotate based on the effects of the surrounding fluid. Through this work, three distinct regimes in the characteristics of the fluid–particle drag force are observed: low, intermediate and high $St$. It is found that, in the low-$Re$ regime, a decrease in $St$ results in a reduction in the fluid–particle drag. Based on the simulation results, a new drag relation is proposed, which is, unlike previous models, dependent on $St$.
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Feng, J., H. H. Hu, and D. D. Joseph. "Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation." Journal of Fluid Mechanics 261 (February 25, 1994): 95–134. http://dx.doi.org/10.1017/s0022112094000285.
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This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.
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Fornari, Walter, Mehdi Niazi Ardekani, and Luca Brandt. "Clustering and increased settling speed of oblate particles at finite Reynolds number." Journal of Fluid Mechanics 848 (June 11, 2018): 696–721. http://dx.doi.org/10.1017/jfm.2018.370.
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We study the settling of rigid oblates in a quiescent fluid using interface-resolved direct numerical simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle–particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio $AR=1/3$ and solid volume fractions $\unicode[STIX]{x1D719}=0.5{-}10\,\%$. The solid-to-fluid density ratio $R=1.02$ and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere with equivalent volume $Ga=60$. With this choice of parameters, an isolated oblate falls vertically with a steady wake with its broad side perpendicular to the gravity direction. At this $Ga$, the mean settling speed of spheres is a decreasing function of the volume $\unicode[STIX]{x1D719}$ and is always smaller than the terminal velocity of the isolated particle, $V_{t}$. On the contrary, in dilute suspensions of oblate particles (with $\unicode[STIX]{x1D719}\leqslant 1\,\%$), the mean settling speed is approximately 33 % larger than $V_{t}$. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity $V_{t}$ between $\unicode[STIX]{x1D719}=5\,\%$ and 10 %. The increase of the mean settling speed is due to the formation of particle clusters that for $\unicode[STIX]{x1D719}=0.5{-}1\,\%$ appear as columnar-like structures. From the pair distribution function we observe that it is most probable to find particle pairs almost vertically aligned. However, the pair distribution function is non-negligible all around the reference particle indicating that there is a substantial amount of clustering at radial distances between 2 and $6c$ (with $c$ the polar radius of the oblate). Above $\unicode[STIX]{x1D719}=5\,\%$, the hindrance becomes the dominant effect, and the mean settling speed decreases below $V_{t}$. As the particle concentration increases, the mean particle orientation changes and the mean pitch angle (the angle between the particle axis of symmetry and gravity) increases from $23^{\circ }$ to $47^{\circ }$. Finally, we increase $Ga$ from 60 to 140 for the case with $\unicode[STIX]{x1D719}=0.5\,\%$ and find that the mean settling speed (normalized by $V_{t}$) decreases by less than 1 % with respect to $Ga=60$. However, the fluctuations of the settling speed around the mean are reduced and the probability of finding vertically aligned particle pairs increases.
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Yin, Zhao-Qin, and Ming Lou. "Experimental study on nanoparticle deposition in straight pipe flow." Thermal Science 16, no. 5 (2012): 1410–13. http://dx.doi.org/10.2298/tsci1205410y.
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Loss of the number of nanoparticles within pipe may lead to significant change of particle number distribution, total mass concentration and particles mean size. The experiments of multiple dispersion aerosol particles ranging from 5.6 nm to 560 nm in straight pipe are carried out using a fast mobility particle sizer. The particle size number distribution, total number concentrations, geometric mean size and volume are acquired under different pipe lengths and Reynolds numbers. The results show lengthening the pipe and strengthening the turbulence can promote the particle deposition process. The penetration efficiency of smaller particle is lower than the larger one, so the particle mean size increases in the process of deposition.
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Kurose, Ryoichi, Hisao Makino, and Satoru Komori. "Particle Trajectory in Turbulent Boundary Layer at High Particle Reynolds Number." Journal of Fluids Engineering 123, no. 4 (May 20, 2001): 956–58. http://dx.doi.org/10.1115/1.1400750.
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H. Sulaymon, Abbas, and Sawsan A. M. Mohammed. "Drag Forces under Longitudinal Interaction of Two Particle." Iraqi Journal of Chemical and Petroleum Engineering 8, no. 2 (June 30, 2007): 1–4. http://dx.doi.org/10.31699/ijcpe.2007.2.1.
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Direct measurements of drag force on two interacting particles arranged in the longitudinal direction for particle Reynolds numbers varying from J O to 103 are conducted using a micro-force measurement system. The effect of the interparticle distance and Reynolds number on the drag forces is examined. An empirical equation is obtained to describe the effect of the interparticle distance (l/d) on the dimensionless drag.
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Ireland, Peter J., Andrew D. Bragg, and Lance R. Collins. "The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects." Journal of Fluid Mechanics 796 (May 11, 2016): 617–58. http://dx.doi.org/10.1017/jfm.2016.238.
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In this study, we analyse the statistics of both individual inertial particles and inertial particle pairs in direct numerical simulations of homogeneous isotropic turbulence in the absence of gravity. The effect of the Taylor microscale Reynolds number, $R_{{\it\lambda}}$, on the particle statistics is examined over the largest range to date (from $R_{{\it\lambda}}=88$ to 597), at small, intermediate and large Kolmogorov-scale Stokes numbers $St$. We first explore the effect of preferential sampling on the single-particle statistics and find that low-$St$ inertial particles are ejected from both vortex tubes and vortex sheets (the latter becoming increasingly prevalent at higher Reynolds numbers) and preferentially accumulate in regions of irrotational dissipation. We use this understanding of preferential sampling to provide a physical explanation for many of the trends in the particle velocity gradients, kinetic energies and accelerations at low $St$, which are well represented by the model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219–251). As $St$ increases, inertial filtering effects become more important, causing the particle kinetic energies and accelerations to decrease. The effect of inertial filtering on the particle kinetic energies and accelerations diminishes with increasing Reynolds number and is well captured by the models of Abrahamson (Chem. Engng Sci., vol. 30, 1975, pp. 1371–1379) and Zaichik & Alipchenkov (Intl J. Multiphase Flow, vol. 34 (9), 2008, pp. 865–868), respectively. We then consider particle-pair statistics, and focus our attention on the relative velocities and radial distribution functions (RDFs) of the particles, with the aim of understanding the underlying physical mechanisms contributing to particle collisions. The relative velocity statistics indicate that preferential sampling effects are important for $St\lesssim 0.1$ and that path-history/non-local effects become increasingly important for $St\gtrsim 0.2$. While higher-order relative velocity statistics are influenced by the increased intermittency of the turbulence at high Reynolds numbers, the lower-order relative velocity statistics are only weakly sensitive to changes in Reynolds number at low $St$. The Reynolds-number trends in these quantities at intermediate and large $St$ are explained based on the influence of the available flow scales on the path-history and inertial filtering effects. We find that the RDFs peak near $St$ of order unity, that they exhibit power-law scaling for low and intermediate $St$ and that they are largely independent of Reynolds number for low and intermediate $St$. We use the model of Zaichik & Alipchenkov (New J. Phys., vol. 11, 2009, 103018) to explain the physical mechanisms responsible for these trends, and find that this model is able to capture the quantitative behaviour of the RDFs extremely well when direct numerical simulation data for the structure functions are specified, in agreement with Bragg & Collins (New J. Phys., vol. 16, 2014a, 055013). We also observe that at large $St$, changes in the RDF are related to changes in the scaling exponents of the relative velocity variances. The particle collision kernel closely matches that computed by Rosa et al. (New J. Phys., vol. 15, 2013, 045032) and is found to be largely insensitive to the flow Reynolds number. This suggests that relatively low-Reynolds-number simulations may be able to capture much of the relevant physics of droplet collisions and growth in the adiabatic cores of atmospheric clouds.
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XIE, M. L., J. Z. LIN, and H. C. ZHOU. "TEMPORAL STABILITY OF A PARTICLE-LADEN BLASIUS BOUNDARY LAYER." Modern Physics Letters B 23, no. 02 (January 20, 2009): 203–16. http://dx.doi.org/10.1142/s0217984909017844.
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The temporal instability of incompressible particle-laden Blasius boundary layer is investigated numerically using perturbation method and finite difference. The stability characteristics are calculated for varying Stokes' numbers and particle concentrations. The results, some of which agree with the calculations of earlier authors, show that the addition of fine particles tends to destabilize the flow while addition of the coarse particles has a stabilizing action. There is critical value for the effect of Stokes' number, and the value is about 1. The stabilizing effect of particles depends monotonously on the particle concentration, the critical Reynolds' number is directly proportional to the concentration in the range of stabilizing area, and vice versa for small Stokes' number. The most damped mode occurs when Stokes' number is of order 10 for different particle concentrations. The difference of perturbation velocity between the particle-laden flow and the clean gas flow is insignificant for fine particles, while the difference for coarse particles is obvious. For fine particles laden flow, the viscosity is reduced relatively because of the addition of particles, and the critical Reynolds' number is smaller than that of clean gas. For coarse particles, the interaction between particles and clean gas is remarkable because of the difference of perturbation velocity, and then the viscous dissipation tends to stabilize the flow.
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Nie, De Ming, and Meng Jiao Zheng. "Computer Simulation of a Drop-Shaped Particle Settling in a Newtonian Fluid." Applied Mechanics and Materials 444-445 (October 2013): 369–73. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.369.
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This work focuses on the effects of the particle shape factor and blockage ratio on the friction coefficient and drag coefficient of the drop-shaped particle for Reynolds number ranging from 10-2 to 102 when the particle is settling under gravity. Comparison with the results of a circular particle has also been presented. It has been shown that the particle friction coefficient keeps constant when Reynolds number is below 1, and increases as Reynolds number increasing when Reynolds number is greater than 1. Furthermore, results have also shown that both the friction coefficient and drag coefficient of the circular particle are smaller than those of the drop-shaped one when Reynolds number is below about 30 while bigger than those of drop-shaped one when Reynolds number is larger than 30.
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Zhao, Lihao, and Helge I. Andersson. "Statistics of Particle Suspensions in Turbulent Channel Flow." Communications in Computational Physics 11, no. 4 (April 2012): 1311–22. http://dx.doi.org/10.4208/cicp.080510.150511s.
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AbstractParticle dynamics in a turbulent channel flow is considered. The effects of particle concentration and Reynolds number on the particle velocity statistics are investigated. Four different particle response times, τ+=1, 5, 30 and 100, are examined for three different Reynolds numbers, Re*=200, 360 and 790 (based on channel height and friction velocity). The particle concentration evolves with time and statistics obtained during three different sampling periods might be distinctly different. The mean and fluctuating particle velocities are substantially affected both by the particle response time and by the Reynolds number of the flow.
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Nie, Deming, Limin Qiu, and Xiaobin Zhang. "Direct numerical simulation of multiple interacting particles at intermediate Reynolds numbers." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 2 (March 2, 2015): 202–13. http://dx.doi.org/10.1108/hff-04-2013-0138.
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Purpose – The purpose of this paper is to study the flow patterns and particle-particle collisions during the sedimentation of multiple circular particles under gravity at intermediate Reynolds numbers through direct numerical simulations (DNS). Design/methodology/approach – The previously developed lattice Boltzmann-direct forcing/fictitious domain (LB-DF/FD) method is adopted in this work to conduct DNS. Findings – It is found that the number of particle-particle collisions display a linear growth at long times after an initial evolution, resulting in a constant collision rate, which also depends the initial arrangement. Originality/value – The problem of particle-particle collisions during sedimentation with two kinds of particle density has not been considered before and it is of special importance in various industries.
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Zandi Pour, Hamid Reza, and Michele Iovieno. "Heat Transfer in a Non-Isothermal Collisionless Turbulent Particle-Laden Flow." Fluids 7, no. 11 (November 7, 2022): 345. http://dx.doi.org/10.3390/fluids7110345.
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To better understand the role of particle inertia on the heat transfer in the presence of a thermal inhomogeneity, Eulerian–Lagrangian direct numerical simulations (DNSs) have been carried out by using the point–particle model. By considering particles transported by a homogeneous and isotropic, statistically steady turbulent velocity field with a Taylor microscale Reynolds number from 37 to 124, we have investigated the role of particle inertia and thermal inertia in one- and two-way coupling collisionless regimes on the heat transfer between two regions at uniform temperature. A wide range of Stokes numbers, from 0.1 to 3 with a thermal Stokes-number-to-Stokes-number ratio equal to 0.5 to 4.43 has been simulated. It has been found that all moments always undergo a self-similar evolution in the interfacial region between the two uniform temperature zones, the thickness of which shows diffusive growth. We have determined that the maximum contribution of particles to the heat flux, relative to the convective heat transfer, is achieved at a Stokes number which increases with the ratio between thermal Stokes and Stokes number, approaching 1 for very large ratios. Furthermore, the maximum increases with the thermal Stokes-to-Stokes number ratio whereas it reduces for increasing Reynolds. In the two-way coupling regime, particle feedback tends to smooth temperature gradients by reducing the convective heat flux and to increase the particle turbulent heat flux, in particular at a high Stokes number. The impact of particle inertia reduces at very large Stokes numbers and at larger Reynolds numbers. The dependence of the Nusselt number on the relevant governing parameters is presented. The implications of these findings for turbulence modelling are also briefly discussed.
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Linares-Guerrero, Esperanza, Melany L. Hunt, and Roberto Zenit. "Effects of inertia and turbulence on rheological measurements of neutrally buoyant suspensions." Journal of Fluid Mechanics 811 (December 13, 2016): 525–43. http://dx.doi.org/10.1017/jfm.2016.763.
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For low-Reynolds-number shear flows of neutrally buoyant suspensions, the shear stress is often modelled using an effective viscosity that depends only on the solid fraction. As the Reynolds number ($Re$) is increased and inertia becomes important, the effective viscosity also depends on the Reynolds number itself. The current experiments measure the torque for flows of neutrally buoyant particles in a coaxial-cylinder rheometer for solid fractions, $\unicode[STIX]{x1D719}$, from 10 % to 50 % and Reynolds numbers based on particle diameter from 2 to 1000. For experiments for Reynolds of $O(10)$ and solid fractions less than $30\,\%$, the effective viscosity increases with Reynolds number, in good agreement with recent numerical simulations found in the literature. At higher solid fractions over the same range of $Re$, the results show a decrease in torque with shear rate. For Reynolds numbers greater than 100 and lower solids concentrations, the effective viscosity continues to increase with Reynolds number. However, based on comparisons with pure fluid measurements the increase in the measured effective viscosity results from the transition to turbulence. The particles augment the turbulence by increasing the magnitude of the measured torques and causing the flow to transition at lower Reynolds numbers. For the highest solid fractions, the measurements show a significant increase in the magnitude of the torques, but the effective viscosity is independent of Reynolds number.
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Espinosa-Gayosso, Alexis, Marco Ghisalberti, Gregory N. Ivey, and Nicole L. Jones. "Particle capture by a circular cylinder in the vortex-shedding regime." Journal of Fluid Mechanics 733 (September 19, 2013): 171–88. http://dx.doi.org/10.1017/jfm.2013.407.
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AbstractParticle capture, whereby suspended particles contact and adhere to a solid surface (a ‘collector’), is an important mechanism for a range of environmental processes including suspension feeding by corals and ‘filtering’ by aquatic vegetation. In this paper, we use two- and three-dimensional direct numerical simulations to quantify the capture efficiency ($\eta $) of low-inertia particles by a circular cylindrical collector at intermediate Reynolds numbers in the vortex-shedding regime (i.e. for $47\lt \mathit{Re}\leq 1000$, where $\mathit{Re}$ is the collector Reynolds number). We demonstrate that vortex shedding induces oscillations near the leading face of the collector which greatly affect the quantity and distribution of captured particles. Unlike in steady, low-$\mathit{Re}$ flow, particles directly upstream of the collector are not the most likely to be captured. Our results demonstrate the dependence of the time-averaged capture efficiency on $\mathit{Re}$ and particle size, improving the predictive capability for the capture of particles by aquatic collectors. The transition to theoretical high-Reynolds-number behaviour (i.e. $\eta \sim {\mathit{Re}}^{1/ 2} $) is complex due to comparatively rapid changes in wake conditions in this Reynolds number range.
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QI, DEWEI. "Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows." Journal of Fluid Mechanics 385 (April 25, 1999): 41–62. http://dx.doi.org/10.1017/s0022112099004401.
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A lattice-Boltzmann method has been developed to simulate suspensions of both spherical and non-spherical particles in finite-Reynolds-number flows. The results for sedimentation of a single elliptical particle are shown to be in excellent agreement with the results of Huang, Hu & Joseph (1998) who used a finite-element method. Sedimentation of two-dimensional circular and rectangular particles in a two-dimensional channel and three-dimensional spherical particles in a tube with square cross-section is simulated. Computational results are consistent with experimentally observed phenomena, such as drafting, kissing and tumbling.
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Zhang, Z., C. Kleinstreuer, and C. S. Kim. "Flow Structure and Particle Transport in a Triple Bifurcation Airway Model1." Journal of Fluids Engineering 123, no. 2 (December 27, 2000): 320–30. http://dx.doi.org/10.1115/1.1359525.
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Considering steady laminar incompressible flow in a triple bifurcation, which represents generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated for several combinations of relatively high and low inlet Reynolds and Stokes numbers. While the upstream bifurcations are hardly affected by the third bifurcation, complex air and particle flow fields occur in the daughter tubes leading to the third dividers. Variations in Reynolds number, 500⩽Re⩽2000, and Stokes number, 0.04⩽St⩽0.12, cause locally changing vortical air flows as well as irregular particle motions. Preferential concentration of particles can be induced by the secondary vortical flow in the tubes when the inlet Reynolds number is high enough. The air and particle velocity profiles in the third daughter tubes are still quite different from those in the upstream tubes, which indicates that additional downstream effects are possible. This work may contribute to respiratory dose estimation in health risk assessment studies, as well as the analyses of drug aerosol delivery.
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Niazi Ardekani, M., O. Abouali, F. Picano, and L. Brandt. "Heat transfer in laminar Couette flow laden with rigid spherical particles." Journal of Fluid Mechanics 834 (November 17, 2017): 308–34. http://dx.doi.org/10.1017/jfm.2017.709.
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We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations. In the simulations we use a direct-forcing immersed boundary method to account for the dispersed phase together with a volume-of-fluid approach to solve the temperature field inside and outside the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed in the literature. In addition, an average composite diffusivity can be used to approximate the effective diffusivity of the suspension in the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, smoothly saturating at higher volume fractions. By phase-ensemble-averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated with fluid and particle velocity. We also show that the contribution of the heat conduction in the solid phase to the total wall-normal heat flux reduces when increasing the particle Reynolds number, so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increases the total heat transfer.
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Duque-Daza, Carlos Alberto, Jesus Ramirez-Pastran, and Santiago Lain. "Influence of Particle Mass Fraction over the Turbulent Behaviour of an Incompressible Particle-Laden Flow." Fluids 6, no. 11 (October 21, 2021): 374. http://dx.doi.org/10.3390/fluids6110374.
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The presence of spherical solid particles immersed in an incompressible turbulent flow was numerically investigated from the perspective of the particle mass fraction (PMF or ϕm), a measure of the particle-to-fluid mass ratio. Although a number of different changes have been reported to be obtained by the presence of solid particles in incompressible turbulent flows, the present study reports the findings of varying ϕm in the the turbulent behaviour of the flow, including aspects such as: turbulent statistics, skin-friction coefficient, and the general dynamics of a particle-laden flow. For this purpose, a particle-laden turbulent channel flow transporting solid particles at three different friction Reynolds numbers, namely Reτ=180, 365, and 950, with a fixed particle volume fraction of ϕv=10−3, was employed as conceptual flow model and simulated using large eddy simulations. The value adopted for ϕv allowed the use of a two-way coupling approach between the particles and the flow or carrier phase. Three different values of ϕm were explored in this work ϕm≈1,2.96, and 12.4. Assessment of the effect of ϕm was performed by examining changes of mean velocity profiles, velocity fluctuation profiles, and a number of other relevant turbulence statistics. Our results show that attenuation of turbulence activity of the carrier phase is attained, and that such attenuation increases with ϕm at fixed Reynolds numbers and ϕv. For the smallest Reynolds number case considered, flows carrying particles with higher ϕm exhibited lower energy requirements to sustain constant fluid mass flow rate conditions. By examining the flow velocity field, as well as instantaneous velocity components contours, it is shown that the attenuation acts even on the largest scales of the flow dynamics, and not only at the smaller levels. These findings reinforce the concept of a selective stabilising effect induced by the solid particles, particularly enhanced by high values of ϕm, which could eventually be exploited for improvement of energetic efficiency of piping or equivalent particles transport systems.
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HAUGEN, NILS ERLAND L., and STEINAR KRAGSET. "Particle impaction on a cylinder in a crossflow as function of Stokes and Reynolds numbers." Journal of Fluid Mechanics 661 (July 27, 2010): 239–61. http://dx.doi.org/10.1017/s0022112010002946.
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A high-order direct numerical simulation code (The Pencil Code) has been used together with the immersed boundary method on a Cartesian grid to simulate particle impaction on a cylinder in a crossflow. The direct numerical scheme concerns only the fluid flow, into which the particles are subsequently coupled through a one-way drag-coefficient law. The immersed boundary method is extended to work with high-order discretization, and the particle impaction efficiency has been measured for Stokes numbers ranging from 0.001 to 40 for a range of different Reynolds numbers. Three modes of impaction on the front side of the cylinder are identified, where, for the large-Stokes-number mode (St > 0.3), an alternative to the traditional Stokes number is presented that provides better scaling. The intermediate impaction mode has a very steep decrease in impaction efficiency as the Stokes number is decreased, and this is identified as the range of Stokes numbers where the viscous boundary layer starts to take effect. The third mode of front-side impaction is for the very small particles with St < 0.1 exactly following the flow but impacting on the cylinder due to their finite radii. There will not be any capture on the front side of the cylinder for impact angles larger than ~56° for this mode. Finally, it is found that the particle impaction on the back side of the cylinder is strongly dependent on the flow Reynolds number, where large Reynolds numbers lead to larger impaction efficiencies. The upper limiting Stokes number of back-side impaction is around 0.13, apparently irrespective of the Reynolds number.
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Gao, Yanfeng, Pascale Magaud, Lucien Baldas, and Yanping Wang. "Inertial Migration of Neutrally Buoyant Spherical Particles in Square Channels at Moderate and High Reynolds Numbers." Micromachines 12, no. 2 (February 14, 2021): 198. http://dx.doi.org/10.3390/mi12020198.
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The inertial migration of particles in microchannel flows has been deeply investigated in the last two decades. In spite of numerous reports on the inertial focusing patterns in a square channel, the particle inertial focusing and longitudinal ordering processes remain unclear at high Reynolds numbers (>200) in square microchannels smaller than 100 µm in width. Thus, in this work, in situ visualization of particles flowing in square micro-channels at Reynolds numbers Re ranging from 5 to 280 has been conducted and their migration behaviors have been analyzed. The obtained results confirm that new equilibrium positions appear above a critical Re depending on the particle to channel size ratio and the particle volume fraction. It is also shown that, for a given channel length, an optimal Reynolds number can be identified, for which the ratio of particles located on equilibrium positions is maximal. Moreover, the longitudinal ordering process, i.e., the formation of trains of particles on equilibrium positions and the characterization of their length, has also been analyzed for the different flow conditions investigated in this study.
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Wang, Ruijin. "Hydrodynamic Trapping of Particles in an Expansion-Contraction Microfluidic Device." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/496243.
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Manipulation and sorting of particles utilizing microfluidic phenomena have been a hot spot in recent years. Here, we present numerical investigations on particle trapping techniques by using intrinsic hydrodynamic effects in an expansion-contraction microfluidic device. One emphasis is on the underlying fluid dynamical mechanisms causing cross-streamlines migration of the particles in shear and vortical flows. The results show us that the expansion-contraction geometric structure is beneficial to particle trapping according to its size. Particle Reynolds number and aspect ratio of the channel will influence the trapping efficiency greatly because the force balance between inertial lift and vortex drag forces is the intrinsic reason. Especially, obvious inline particles contribution presented when the particle Reynolds number being unit. In addition, we selected three particle sizes (2, 7, and 15 μm) to examine the trapping efficiency.
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Chtab, Anna, and Mikhael Gorokhovski. "Large-Eddy Simulation With Simplified Collisional Microdynamics in a High Reynolds Number Particle-Laden Channel Flow." Journal of Fluids Engineering 129, no. 5 (October 25, 2006): 613–20. http://dx.doi.org/10.1115/1.2717619.
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Computing high Reynolds number channel flows laden by heavy solid particles requires excessive CPU resources to calculate interparticle collisions. Since the frequency of these collisions is high, the kinematic details of each elementary collision may not be essential when calculating particle statistics. In this paper, the dynamics of a particle with a phase trajectory that is discontinuous (due to collisions) is simulated using a hypothetical “noncolliding” particle moving along a trajectory smoothed over interparticle collisions. The statistical temperature of this particle is assumed to be in equilibrium with the statistical “temperature” of the resolved turbulence. This simplified microdynamic is introduced into ballistic calculations of particles within the framework of the “two-way” LES approach. The simulation was conducted specifically to compare the velocity statistics of the hypothetical particle with statistics yielded by measurements in the gas∕particle channel flow and by the LES∕particle approach where binary collisions were simulated. This paper shows that, by assuming the universality of collisional microdynamics, one may predict the experimental observation and the results of detailed simulations without requiring supplementary CPU resources to compute the binary collisions.
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Wang, Zekun, Khuram Walayat, and Moubin Liu. "A velocity corrected unresolved CFD-DEM coupled method to reproduce wake effects at moderate Reynolds number." Engineering Computations 36, no. 8 (October 7, 2019): 2612–33. http://dx.doi.org/10.1108/ec-10-2018-0454.
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Purpose The purpose of this paper is to develop a corrected unresolved CFD-DEM method that can reproduce the wake effects in modeling particulate flows at moderate Reynolds number. Design/methodology/approach First, the velocity field in the wake behind a settling particle is numerically investigated by a resolved method, in which the finite volume method (FVM) is applied to model the fluid flow, discrete element method (DEM) is applied to simulate the motion of particles and immersed boundary method (IBM) is used to tackle fluid solid interaction. Second, an analytical scaling law is given, which can effectively describe the velocity field in the wake behind the settling particle at low and middle Reynolds numbers. Third, this analytical expression is incorporated into unresolved modeling to correct the relative velocity between the particle and its surrounding fluid and enable the influence of the wake of the particle on its neighboring particles. Findings Two numerical examples, the sedimentation of dual particles, a list of particles and even more particles are provided to show the effectiveness of the presented velocity corrected unresolved method (VCUM). It is found that, in both examples simulated with VCUM, the relative positions of the particles changed, and drafting & kissing phenomenon and particle clustering phenomenon were clearly observed. Practical implications The developed VCUM can be highly beneficial for modeling industrial particulate flows with DKT and particle clustering phenomena. Originality/value VCUM innovatively incorporates the wake effects into unresolved CFD-DEM method. It improves the computational accuracy of conventional unresolved methods with comparable results from resolved modeling, while the computational cost is greatly reduced.
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CHOI, HYOUNG G., and DANIEL D. JOSEPH. "Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation." Journal of Fluid Mechanics 438 (July 5, 2001): 101–28. http://dx.doi.org/10.1017/s0022112001004177.
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We study the transport of a slurry of heavier-than-liquid circular particles in a plane pressure-driven flow in a direct simulation. The flow is calculated in a periodic domain containing 300 circular particles. The study leads to the concept of fluidization by lift in which all the particles are suspended by lift forces against gravity perpendicular to the flow. The study is framed as an initial-value problem in which a closely packed cubic array of particles resting on the bottom of the channel is lifted into suspension. All the details of the flow are resolved numerically without model assumptions. The fluidization of circular particles first involves bed inflation in which liquid is driven into the bed by high pressure at the front and low pressure at the back of each circle in the top row. This kind of bed inflation occurs even at very low Reynolds numbers but it takes more time for the bed to inflate as the Reynolds number is reduced. It appears that the bed will not inflate if the shear Reynolds number is below the critical value for single particle lift-off. The flows with a single particle are completely determined by a shear Reynolds number and a gravity parameter when the density ratio and aspect ratio parameters are specified. In the multi-particle case, the volume fraction and distribution also matters. The transition to a fully fluidized slurry by waves is discussed.An analytical model of the steady motion of a single particle dragged forward in a Poiseuille flow is derived and compared with a simulation. The undisturbed fluid velocity is always larger than the particle velocity, producing a fluid hold-up. The effect of the hold-up in the many particle case is to greatly reduce the velocity of the mixture which may be described by a two-fluid model in which the solid laden mixture is regarded as a second fluid with effective properties.
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Collins, Lance R., and Arun Keswani. "Reynolds number scaling of particle clustering in turbulent aerosols." New Journal of Physics 6 (September 18, 2004): 119. http://dx.doi.org/10.1088/1367-2630/6/1/119.
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Meister, Michael, Gregor Burger, and Wolfgang Rauch. "On the Reynolds number sensitivity of smoothed particle hydrodynamics." Journal of Hydraulic Research 52, no. 6 (September 15, 2014): 824–35. http://dx.doi.org/10.1080/00221686.2014.932855.
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Blake, T. R. "Low reynolds number combustion of a spherical carbon particle." Combustion and Flame 129, no. 1-2 (April 2002): 87–111. http://dx.doi.org/10.1016/s0010-2180(01)00360-1.
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Park, Ki Sun, and Stephen D. Heister. "Modeling particle collision processes in high Reynolds number flow." Journal of Aerosol Science 66 (December 2013): 123–38. http://dx.doi.org/10.1016/j.jaerosci.2013.08.010.
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Yu, Zhaosheng, Peng Wang, Jianzhong Lin, and Howard H. Hu. "Equilibrium positions of the elasto-inertial particle migration in rectangular channel flow of Oldroyd-B viscoelastic fluids." Journal of Fluid Mechanics 868 (April 11, 2019): 316–40. http://dx.doi.org/10.1017/jfm.2019.188.
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In this paper, the lateral migration of a neutrally buoyant spherical particle in the pressure-driven rectangular channel flow of an Oldroyd-B fluid is numerically investigated with a fictitious domain method. The aspect ratio of the channel cross-section considered is 1 and 2, respectively. The particle lateral motion trajectories are shown for the bulk Reynolds number ranging from 1 to 100, the ratio of the solvent viscosity to the total viscosity being 0.5, and a Weissenberg number up to 1.5. Our results indicate that the lateral equilibrium positions located on the cross-section midline, diagonal line, corner and channel centreline occur successively as the fluid elasticity is increased, for particle migration in square channel flow with finite fluid inertia. The transition of the equilibrium position depends strongly on the elasticity number (the ratio of the Weissenberg number to the Reynolds number) and weakly on the Reynolds number. The diagonal-line equilibrium position occurs at an elasticity number ranging from roughly 0.001 to 0.02, and can coexist with the midline and corner equilibrium positions. When the fluid inertia is negligibly small, particles migrate towards the channel centreline, or the closest corner, depending on their initial positions and the Weissenberg number, and the corner attractive area first increases and then decreases as the Weissenberg number increases. For particle migration in a rectangular channel with an aspect ratio of 2, the transition of the equilibrium position from the midline, ‘diagonal line’ (the line where two lateral shear rates are equal to each other), off-centre long midline and channel centreline takes place as the Weissenberg number increases at moderate Reynolds numbers. An off-centre equilibrium position on the long midline is observed for a large blockage ratio of 0.3 (i.e. the ratio of the particle diameter to the channel height is 0.3) at a low Reynolds number. This off-centre migration is driven by shear forces, unlike the elasticity-induced rapid inward migration, which is driven by the normal force (pressure or first normal stress difference).
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Nirschl, H., H. A. Dwyer, and V. Denk. "Three-dimensional calculations of the simple shear flow around a single particle between two moving walls." Journal of Fluid Mechanics 283 (January 25, 1995): 273–85. http://dx.doi.org/10.1017/s002211209500231x.
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Three-dimensional solutions have been obtained for the steady simple shear flow over a spherical particle in the intermediate Reynolds number range 0.1 [les ] Re [les ] 100. The shear flow was generated by two walls which move at the same speed but in opposite directions, and the particle was located in the middle of the gap between the walls. The particle-wall interaction is treated by introducing a fully three-dimensional Chimera or overset grid scheme. The Chimera grid scheme allows each component of a flow to be accurately and efficiently treated. For low Reynolds numbers and without any wall influence we have verified the solution of Taylor (1932) for the shear around a rigid sphere. With increasing Reynolds numbers the angular velocity for zero moment for the sphere decreases with increasing Reynolds number. The influence of the wall has been quantified with the global particle surface characteristics such as net torque and Nusselt number. A detailed analysis of the influence of the wall distance and Reynolds number on the surface distributions of pressure, shear stress and heat transfer has also been carried out.
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PATANKAR, N. A., P. Y. HUANG, T. KO, and D. D. JOSEPH. "Lift-off of a single particle in Newtonian and viscoelastic fluids by direct numerical simulation." Journal of Fluid Mechanics 438 (July 5, 2001): 67–100. http://dx.doi.org/10.1017/s0022112001004104.
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In this paper we study the lift-off to equilibrium of a single circular particle in Newtonian and viscoelastic fluids by direct numerical simulation. A particle heavier than the fluid is driven forward on the bottom of a channel by a plane Poiseuille flow. After a certain critical Reynolds number, the particle rises from the wall to an equilibrium height at which the buoyant weight just balances the upward thrust from the hydrodynamic force. The aim of the calculation is the determination of the critical lift-off condition and the evolution of the height, velocity and angular velocity of the particle as a function of the pressure gradient and material and geometric parameters. The critical Reynolds number for lift-off is found to be larger for a heavier particle whereas it is lower for a particle in a viscoelastic fluid. A correlation for the critical shear Reynolds number for lift-off is obtained. The equilibrium height increases with the Reynolds number, the fluid elasticity and the slip angular velocity of the particle. Simulations of single particle lift-off at higher Reynolds numbers in a Newtonian fluid by Choi & Joseph (2001) but reported here show multiple steady states and hysteresis loops. This is shown here to be due to the presence of two turning points of the equilibrium solution.
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Li, Xiaohui, Guodong Liu, Junnan Zhao, Xiaolong Yin, and Huilin Lu. "IBM-LBM-DEM Study of Two-Particle Sedimentation: Drafting-Kissing-Tumbling and Effects of Particle Reynolds Number and Initial Positions of Particles." Energies 15, no. 9 (April 30, 2022): 3297. http://dx.doi.org/10.3390/en15093297.
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Particle sedimentation is a fundamental process encountered in various industrial applications. In this study, we used immersed boundary lattice Boltzmann method and discrete element method (IBM-LBM-DEM) to investigate two-particle sedimentation. A lattice Boltzmann method was used to simulate fluid flow, a discrete element method was used to simulate particle dynamics, and an immersed boundary method was used to handle particle–fluid interactions. Via the IBM-LBM-DEM, the particles collision process in fluid or between rigid walls can be calculated to capture the information of particles and the flow field more efficiently and accurately. The numerical method was verified by simulating settling of a single three-dimensional particle. Then, the effects of Reynolds number (Re), initial distance, and initial angle of particles on two-particle sedimentation were characterized. A specific focus was to reproduce, analyze, and define the well-known phenomenon of drafting-kissing-tumbling (DKT) interaction between two particles. Further kinematic analysis to define DKT is meaningful for two-particle sedimentation studies at different particle locations. Whether a pair of particles has experienced DKT can be viewed from time plots of the distance between the particles (for kissing), the second-order derivative of distance to time (for drafting), and angular velocities of particles (for tumbling). Simulation results show that DKT’s signatures, including attraction, (near) contact, rotation, and in the end, separation, is only completely demonstrated when particles have nearly vertically aligned initial positions. Hence, not all initial positions of particles and Reynolds numbers lead to DKT and not all particle–particle hydrodynamic interactions are DKT. Whether particle–particle interaction is attractive or repulsive depends on the relative positions of particles and Re. Collision occurs when Re is high and the initial angle is small (<20°), almost independent of the initial distance.
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Shao, Xueming, Tenghu Wu, and Zhaosheng Yu. "Fully resolved numerical simulation of particle-laden turbulent flow in a horizontal channel at a low Reynolds number." Journal of Fluid Mechanics 693 (January 17, 2012): 319–44. http://dx.doi.org/10.1017/jfm.2011.533.
Full textAbstract:
AbstractA fictitious domain method is used to perform fully resolved numerical simulations of particle-laden turbulent flow in a horizontal channel. The effects of large particles of diameter 0.05 and 0.1 times the channel height on the turbulence statistics and structures are investigated for different settling coefficients and volume fractions (0.79 %–7.08 %) for the channel Reynolds number being 5000. The results indicate the following. (a) When the particle sedimentation effect is negligible (i.e. neutrally buoyant), the presence of particles decreases the maximum r.m.s. of streamwise velocity fluctuation near the wall by weakening the intensity of the large-scale streamwise vortices, while increasing the r.m.s. of the streamwise fluctuating velocity in the region very close to the wall and in the centre region. On the other hand, the particles increase the r.m.s. of transverse and spanwise fluctuating velocities in the near-wall region by inducing the small-scale vortices. (b) When the particle settling effect is so substantial that most particles settle onto the bottom wall and form a particle sediment layer (SL), the SL plays the role of a rough wall and parts of the vortex structures shedding from the SL ascend into the core region and substantially increase the turbulence intensity there. (c) When the particle settling effect is moderate, the effects of particles on the turbulence are a combination of the former two situations, and the Shields number is a good parameter for measuring the particle settling effects (i.e. the particle concentration distribution in the transverse direction). The average velocities of the particle are smaller in the lower half-channel and larger in the upper half-channel compared to the local fluid velocities in the presence of gravity effects. The effects of the smaller particles on the turbulence are found to be stronger at the same particle volume fractions.