Particle-fluid Density Ratio Research Articles

Effect of instantaneous local solid volume fraction on hydrodynamic forces in freely evolving particle suspensions

Particle Resolved Simulations (PRS) for freely evolving sphere suspensions at solid volume fractions (φ) between 0.1 and 0.4, Reynolds number Re from 10 to 300 and particle-fluid density ratios ρsρf of 2, 10 and 100 are used to investigate the effect of Voronoi tessellation based particle local solid volume fraction (φv)on particle drag and lateral forces. Findings reveal the instantaneous suspension mean drag force is positively correlated with the variance of φv among particles in the suspension. It is also shown that using the conditioned instantaneous φv of each particle in existing mean drag force correlations can significantly improve the prediction accuracy. Suspension mean lateral force ranges up to 60 % of the drag force while individual particles exhibit values as high as 90 % of the drag force. An instantaneous lateral force correlation is proposed based on suspension-averaged flow variables and φv.

Dissipation Effects in the Tea Leaf Paradox

The Tea Leaf Paradox (TLP) describes unsteady fluid motions which help entrain and deposit suspended particles at the center of rotation. Various applications depend on the TLP for particle separations—spanning orders of magnitude in length scales—making it an important problem in fluid mechanics. Despite papers describing the phenomenon, the efficacy of particle separation using the TLP remains unclear as to the relative importance of, for example, hydrostatics, particle-fluid density ratio, wall friction, liquid bath aspect ratio and the rotation speed. The dynamics involved are notably complex and require a careful tuning of each variable. In this study, we have investigated the role of the limit of the aggregation dynamics in rotational flows within 3D-printed vessels of various sizes in tandem with particle imaging to probe the dissipation effects on the particle motions. We have found that the liquid bath aspect ratio limits how much aggregation may occur for a particle-fluid density ratio greater than unity (e.g., ρp/ρf>1), where ρp is the density of the particle and ρf is the ambient fluid density.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Stokes drift and impurity transport in a quantum fluid

Stokes drift is a classical fluid effect in which traveling waves transfer momentum to tracers of the fluid, resulting in a nonzero drift velocity in the direction of the incoming wave; this effect is the driving mechanism allowing particles, i.e., impurities, to be transported by the flow. In a classical (viscous) fluid this happens usually due to the presence of viscous drag forces; because of the eventual absence of viscosity in quantum fluids, impurities are driven by inertial effects and pressure gradients only. We present theoretical predictions of a Stokes drift analogous in quantum fluids finding that, at the leading order, the drift direction and amplitude depend on the initial impurity position with respect to the wave phase, and at the second order, our theoretical model recovers the classical Stokes drift but with a coefficient that depends on the relative particle-fluid density ratio. Our theoretical predictions are obtained for classical impurities using multitime analytical asymptotic expansions. Numerical simulations of a two-dimensional Gross-Pitaevskii equation coupled with a classical impurity corroborate our findings. Our findings are experimentally testable, for instance, using fluids of light obtained in photorefractive crystals.Received 15 December 2022Revised 19 April 2023Accepted 17 May 2023DOI:https://doi.org/10.1103/PhysRevA.107.L061303Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFluid-particle interactionsPhysical SystemsQuantum fluids & solidsSuperfluidsUltracold gasesTechniquesPerturbative methodsNonlinear DynamicsFluid DynamicsAtomic, Molecular & Optical

Scaling laws for planetary sediment transport from DEM-RANS numerical simulations

We use an established discrete element method (DEM) Reynolds-averaged Navier–Stokes (RANS)-based numerical model to simulate non-suspended sediment transport across conditions encompassing almost seven orders of magnitude in the particle–fluid density ratio$s$, ranging from subaqueous transport ($s=2.65$) to aeolian transport in the highly rarefied atmosphere of Pluto ($s=10^7$), whereas previous DEM-based sediment transport studies did not exceed terrestrial aeolian conditions ($s\approx 2000$). Guided by these simulations and by experiments, we semi-empirically derive simple scaling laws for the cessation threshold and rate of equilibrium aeolian transport, both exhibiting a rather unusual$s^{1/3}$-dependence. They constitute a simple means to make predictions of aeolian processes across a large range of planetary conditions. The derivation consists of a first-principle-based proof of the statement that, under relatively mild assumptions, the cessation threshold physics is controlled by only one dimensionless control parameter, rather than two expected from dimensional analysis. Crucially, unlike existing models, this proof does not resort to coarse-graining the particle phase of the aeolian transport layer above the bed surface. From the pool of existing models, only that by Pähtzet al.(J. Geophys. Res.: Earth, vol. 126, 2021, e2020JF005859) is somewhat consistent with the combined numerical and experimental data. It captures the scaling of the cessation threshold and the$s^{1/3}$-dependence of the transport rate, but fails to capture the latter's superimposed grain size dependence. This hints at a lack of understanding of the transport rate physics and calls for future studies on this issue.

Anomalous Scaling of Aeolian Sand Transport Reveals Coupling to Bed Rheology

Predicting transport rates of windblown sand is a central problem in aeolian research, with implications for climate, environmental, and planetary sciences. Though studied since the 1930s, the underlying many-body dynamics is still incompletely understood, as underscored by the recent empirical discovery of an unexpected third-root scaling in the particle-fluid density ratio. Here, by means of grain-scale simulations and analytical modeling, we elucidate how a complex coupling between grain-bed collisions and granular creep within the sand bed yields a dilatancy-enhanced bed erodibility. Our minimal saltation model robustly predicts both the observed scaling and a new undersaturated steady transport state that we confirm by simulations for rarefied atmospheres.

Effect of the Stokes boundary layer on the dynamics of particle pairs in an oscillatory flow

The alignment of a pair of spherical particles perpendicular to a horizontally oscillating flow is attributed to a non-zero residual flow, known as steady streaming. This phenomenon is the basis of complex patterns in denser systems, such as particle chains and the initial stages of rolling-grain ripples. Previous studies on such self-organization processes used two distinct systems: an oscillating box filled with viscous fluid and an oscillating channel flow, where the fluid oscillates relative to the bottom boundary. In this paper, we show that particle pair dynamics in these two systems are fundamentally different, due to the presence of a Stokes boundary layer above the bottom in the oscillating channel flow. The results are obtained from direct numerical simulations in which the dynamics of a pair of particles are simulated using an immersed boundary method. The oscillating box and the oscillating channel flow are only equivalent in a limited region of the parameter space, where both the normalized Stokes boundary layer thickness and the normalized relative particle excursion length are small. Overall, the particle dynamics in the oscillating channel flow, compared to the oscillating box, are governed by an additional dimensionless parameter, that is, the particle–fluid density ratio.

Turbulence modulation by finite-size particles of different diameters and particle–fluid density ratios in homogeneous isotropic turbulence

In this paper, the influence of particle-fluid density ratio and particle diameter on the turbulence modulation by finite-size particles in forced homogeneous isotropic turbulence is investigated. Results show that the presence of finite-size particles always attenuate the turbulence, and the attenuation is larger for particles with larger density when the particle diameter is fixed. But the attenuation is smaller for particles with larger diameter if the density is fixed, and the weaker attenuation is due to the wake fluctuation when the particle Reynolds number is large enough. The turbulence kinetic energy is attenuated at the large scales and augmented at the small scales. The radial dissipation profiles show that the region affected by the particles with same diameter is identical, but the dissipation near the particle surface is larger if the density is larger due to larger slip velocity and particle Reynolds number. For particles with same density, smaller particles have smaller dissipation near the particle surface but the influence region is larger, and the combined effect leads to the result that the contribution of dissipation in the influence region of smaller particles to the total dissipation is larger. The influence region mainly depends on the particle diameter.

Periodically driven spheroid in a viscous fluid at low Reynolds numbers

In this paper, we study the motion of a spheroid of a moderate aspect ratio in a viscous fluid under the action of an external harmonic force. We first derive the dynamics equation of the particle oscillating along one of its axes and subject to damping, Basset memory, and second history integral forces at small Reynolds numbers, and then, we proceed to obtain an analytical solution of this equation at resonance. With graphical representation, we observe that for a prolate spheroid, the conventional Q-curves show a greater variation with respect to the particle aspect ratio, particle–fluid density ratio, and natural frequency; the variation is significantly larger for the curve corresponding to the second history force. Furthermore, we find that all three forces affect the amplitude of motion: the amplitude increases with the strength of damping as well as the second history integral forces, whereas the presence of Basset memory decreases it. Remarkably, Basset memory causes a phase-shift in the oscillations, while the other two forces have no effect on the phase. Since our solutions are analytical, they may have valuable application in experiments involving more complex systems, in particular, to understand the effect of external force on the transport of micro-particles.

A coupled distributed Lagrange multiplier (DLM) and discrete element method (DEM) approach to simulate particulate flow with collisions

In this paper, a coupled DLM-DEM numerical approach is proposed to enable particle-particle and particle-wall interactions within the open-source IBAMR (Immersed Boundary Adaptive Mesh Refinement) framework. A soft-sphere DEM collision model is adopted and compared against the particle-particle repulsion force model suggested in the literature. It is demonstrated that the former collision model remains effective at both low and high particle-fluid density ratios, whereas the latter model can lead to unphysical particle-particle interaction dynamics at high density ratios. Moreover, the soft-sphere DEM collision model is based on physical material properties, which is in contrast to an artificial parameter-based repulsion force model. The proposed DLM-DEM approach is validated by simulating the particle-particle collision in drafting, kissing, and tumbling (DKT) phenomenon, and particle-wall collision at various Stokes numbers. Using this approach, we also simulate the interactions between a single colliding particle and a particle cluster and analyze the particles' motion and distribution. Additionally, sedimentation of polygon-shaped particles is also considered to demonstrate the versatility of the proposed approach.

Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows.

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-fluid density ratios respond to the turbulence. Overall particle dynamics in the homogeneous isotropic turbulence such as the Lagrangian statistics of single particle and the preferential concentration of particles are investigated. Results show that particle acceleration and angular acceleration are more intermittent than velocity and angular velocity for finite-size particles with different particle-fluid density ratios. The preferential concentration of particles is investigated using radial distribution function and Voronoï tessellation, and the preferential concentration is more profound for particles with two intermediate particle-fluid density ratios. The Voronoï analysis indicates that the distribution of Voronoï cells satisfy the log-normal distribution better than the gamma distribution. The mechanism of preferential concentration is analyzed using the sweep-stick mechanism and drift mechanism. Results show that although a higher probability of having particles located near the sticky points is found, the sticky mechanism is very weak for large density ratios. The particle clustering is then found to be better qualitatively described by the drift mechanism.

A Functional Form for Fine Sediment Interception in Vegetated Environments

The body of literature seeking to evaluate particle interception in vegetated, aquatic environments is growing; however, comparing the results of these studies is difficult due to large variation in flow regime, particle size, vegetation canopy density, and stem configuration. In this work, we synthesize data from these studies and develop a functional form of particle interception efficiency (η) as a function of stem Reynolds number (Rec), stem diameter, vegetation frontal area, particle–collector diameter ratio, flow velocity, and kinematic viscosity. We develop this functional relationship based on a dimensional analysis and hypothesize that the coefficients would exhibit regimes within different Rec ranges. We test this hypothesis by synthesizing data from 80 flume experiments reported in the literature and in-house flume experiments. Contrary to our hypothesis, data from different Rec ranges follow a single functional form for particle interception. In this form, η varies strongly with collector density and particle–collector diameter ratio, and weakly with Rec and particle–fluid density ratio. This work enables more accurate modeling of the flux terms in sedimentation budgets, which can inform ongoing modeling and management efforts in marsh environments. For example, we show that by integrating the new functional form of particle interception into established models of marsh elevation change, interception may account for up to 60% of total sedimentation in a typical silt-dominated marsh ecosystem with emergent vegetation.

Modulation of turbulence intensity by heavy finite-size particles in upward channel flow

Abstract

Equilibrium sediment transport, grade and discharge for suspended-load-dominated flows on Earth, Mars and Titan

Recent surface observations have emphasised the importance of bedload transport by rivers and streams on Mars and Titan. Previous “hydraulic” analysis, however, has also shown that transport as suspended load should be possible, if not more prevalent due to lower critical shear stresses, under reduced gravity conditions compared with Earth; where the dominant mode of sediment flux by rivers is as suspended load. A new suspended-load equilibrium condition (zero net erosion and deposition) constraint is advanced, using a flux-balance model applicable to transport (capacity) limited alluvial channels. The theory unifies Gilbert's relation for slope and flow capacity model with the Shields criterion for incipient motion. Shields-stress analysis shows that sediment transport thresholds on Earth, Mars and Titan are dynamically similar. Thus, despite large differences in dimensional shear stresses, variations in the critical slopes and flow depths required for threshold and equilibrium conditions are comparatively modest. Under reduced gravity conditions, there exists a slightly higher potential for sediment transport as suspended load; except for systems involving high particle-fluid density ratios, as may apply to the transport of organic particles on Titan. Critically we show that graded suspended-load channels should develop gentler slopes under reduced gravity, and not steeper slopes as previously inferred based on generalized hydraulic geometry relationships of terrestrial river and submarine channels. We further argue that the use of submarine channels as analogues for channels formed under reduced gravity is not physically justified. Finally, compared with bedload channels, suspended-load channels should also have markedly higher discharges, with implications for mechanistic-based discharge predictions and precipitation models.

Direct numerical simulation of turbulent liquid–solid flow in a small-scale stirred tank

Particle-resolved direct numerical simulation of a 4-baffled cylindrical stirred tank with a 6-pitched blade-turbine-downflow (PBTD) impeller was carried out for the first time to understand the hydrodynamic characteristics of its turbulent solid–liquid flow. The fluid-particle and fluid-wall interactions are numerically described by the immersed boundary method (IBM) with smeared and sharp interfaces jointly on a staggered Cartesian grid. The particle diameter is 1 mm, and the impeller rotation speed changes between 23.88 and 15.88 rev/s, resulting in the impeller Reynolds number at 7031 and 4676, respectively, belonging to medium turbulent regime. The average solid volume fraction ranged from 0 to 0.1. The effect of particle inertia was also investigated by changing the particle–fluid density ratio from 1.5 to 3.0. Analysis of the simulation results indicates turbulence suppression in the bulk region and particle-induced strengthening of the axial liquid circulation. The quasi-steady and unsteady drag is correlated to the relative turbulence intensity and the turbulence dissipation rate obtained from the simulation data, respectively.

Oscillations of a periodically forced slightly eccentric spheroid in an unsteady viscous flow at low Reynolds numbers

The equations governing the dynamics of a periodically driven micro-spheroid in an unsteady viscous fluid at low Reynolds number are derived. Its oscillation properties in the presence/absence of memory forces are reported. The core part of the derivation is a perturbation analysis of motion of a sphere. The calculated solutions match with those available in the literature in the limiting case of a sphere. The dependence of the solutions on shape ( $$\alpha $$ ), free oscillation frequency ( $$\omega _0$$ ) and particle–fluid density ratio ( $$d_r$$ ) is calculated. The maximum amplitude of the oscillations of an oblate spheroid is greater than that of a prolate spheroid, showing that the velocity disturbance for an oblate spheroid is higher in the presence/absence of the memory force. The increase in $$\alpha $$ leads to the enhancement(reduction) of amplitude peaks in the case of the oblate (prolate) spheroid in the presence and more dominantly in the absence of the force. There is also a reduction in the amplitude of spheroid oscillations of many multiples due to the presence of the memory force. Stronger oscillation variations are observed on changing $$\omega _0$$ or $$d_r$$ compared to $$\alpha .$$ The variations of the value of the phase are similar for both the spheroids on varying $$\omega _0$$ and $$d_r$$ , whereas they are reversed on varying $$\alpha .$$ The linear scaling of amplitude on $$\alpha $$ observed for the spheroids may give insight into the physics, especially regarding the quantum of velocity disturbances due to particle size. The slopes are high in the absence of the force, confirming that the presence of the force increases the resistance of spheroid motion, largely. The dependencies of oscillations on the parameters can be utilized for better separation of particles or for characterizing the suspension. The novelty of the problem and its analytical solutions might have value as tests in software for more complicated and realistic systems and hence strikes a good balance between complication and tractability.

Scaling law of contact time for particles settling in a quiescent fluid

Numerical simulations are conducted for the gravity–driven settling of two particles in a viscous quiescent fluid. A method is proposed to determine the scaling law of inter–particle contact time. The method is simple and general. The resulting scaling law explains the observations of literature and predicts the influences of particle–fluid density ratio, fluid viscosity, friction, rolling friction, and adhesion force.

A fictitious domain method for particulate flows of arbitrary density ratio

In this paper, our previous direct-forcing fictitious domain method is modified for particle-laden flows of arbitrary density ratio. The instability of original scheme for low density ratio is circumvented by a simple modification in the particle motion equations, with the key idea of increasing the coefficient of particle inertial term. Three schemes are proposed, which are shown to be equally accurate. The modified DF/FD method is extensively validated with various tests, and it is shown that the accuracy of our method is comparable to previous methods. In addition, our method is applied to the direct numerical simulations of the motion of finite-size particles (or bubbles) in a vertical turbulent channel flow of the density ratio 0.001. Our results indicate that the effects of particle-fluid density ratio on turbulent channel flow are negligibly small when the density ratio is smaller than unity and the gravity effect is not considered. The fluid Reynolds shear stress and the wall friction are enhanced in upflow where the particles are aggregated near the wall, whereas they are reduced in downflow where the particles move towards the channel center.

Inertial impaction of particles on a circular cylinder for a wide range of Reynolds and P numbers: A comparative study

In this paper, particulate gas flows over a circular cylinder were studied numerically for wide ranges of flow Reynolds numbers (5 < Re < 5 × 106) and P numbers (0.025 < P < 5 × 104). P number is defined as 9Re/S and S is the particle-fluid density ratio. For Re ≤ 100, the laminar flow simulations were performed while the turbulent flow simulations were done for Re ≥ 103 using unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The Reynolds stress model (RSM) was used to account for the anisotropic turbulent stresses around the cylinder. The computed drag was compared with the available experimental data and earlier numerical results. It was shown that the RSM could properly predict the drag-drop at the critical flow regime. Deposition of particles on the cylinder surface was also investigated using the Lagrangian trajectory analysis. Particle capture efficiencies were evaluated and compared with the available experimental data and theoretical models. The simulation results indicated that for P ≥ 102, the computed capture efficiencies obtained by the viscous flow analysis coincided with those obtained from the inviscid flows. For 1 ≤ P ≤ 10, differences between viscous and inviscid flow collection efficiencies, however, were more than 20% when Stk≤1. However, for P ≤ 0.1, differences between the collection efficiencies obtained by viscous and inviscid flows exceeded 20% when Stk≤2.2. In the case of Re = 103 and P = 10, the highest capture efficiency was obtained by impaction for Stk≥0.5.

Effect of particle density in turbulent channel flows with resolved oblate spheroids

The present paper studies the effect of particle density in a turbulent channel flow laden with resolved oblate spheroids at a frictional Reynolds number of Reτ=180. Direct numerical simulations are performed by using the lattice Boltzmann method (LBM) for solving the flow field. Particle-fluid interactions are modeled by the immersed boundary method (IBM). Simulations are done for dense regimes of heavy and neutrally-buoyant particles with a volume fraction of 5%. The particle-fluid density ratios are 8.0 and 1.0 for heavy and neutrally-buoyant particles, respectively. Results show that particle inertia can significantly modify the fluid and particle statistics. Heavy particles cause a higher reduction of the fluid streamwise velocity with respect to the single-phase flow. Turbulence is attenuated by both particle types but the reduction is stronger with heavy particles than that with neutrally-buoyant ones. Moreover, increasing the density of particles is found to create smaller but more energetic vortices. Quadrant analysis shows that the contribution of ejection and sweep events in the Reynolds shear stress reduce on increasing the particle density. The local volume fractions of the two particle types are also seen to be different. While the volume fraction of neutrally-buoyant particles reach a constant value at a certain distance from the walls, the concentration of heavy oblate spheroids increases gradually all the way up to channel center. Both particle types show preferential orientation near the walls, where the symmetry axis is normal to the wall. However, this preferential orientation is less pronounced when increasing the particle inertia. Finally, the translational velocity fluctuations of heavy particles are found to be higher in the streamwise direction, but lower in the wall-normal direction.