Title: Drag force in granular shear flows: regimes, scaling laws and implications for segregation

The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations. more »« less

Jing, Lu; Ottino, Julio M.; Lueptow, Richard M.; Umbanhowar, Paul B.(
, Journal of Fluid Mechanics)

null
(Ed.)

Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using discrete element method simulations, we show that segregation of a single particle intruder can be described in a unified manner across different flow configurations. A scaling relation for the net segregation force is obtained by measuring forces on an intruder particle in controlled-velocity flows where gravity and flow kinematics are varied independently. The scaling law consists of two additive terms: a buoyancy-like gravity-induced pressure gradient term and a shear rate gradient term, both of which depend on the particle size ratio. The shear rate gradient term reflects a kinematics-driven mechanism whereby larger (smaller) intruders are pushed toward higher (lower) shear rate regions. The scaling is validated, without refitting, in wall-driven flows, inclined wall-driven flows, vertical silo flows, and free-surface flows down inclines. Comparing the segregation force with the intruder weight results in predictions of the segregation direction that match experimental and computational results for various flow configurations.

Jing, Lu; Ottino, Julio M.; Lueptow, Richard M.; Umbanhowar, Paul B.(
, EPJ Web of Conferences)

Aguirre, M.A.; Luding, S.; Pugnaloni, L.A.; Soto, R.
(Ed.)

Particle segregation in geophysical and industrial granular flows is typically driven by gravity and shear. While gravity-induced segregation is relatively well understood, shear-induced segregation is not. In particular, what controls segregation in the absence of gravity and the interplay between shearand gravity-driven segregation remain unclear. Here, we explore the shear-induced segregation force on an intruder particle in controlled-velocity granular flows where the shear profile is systematically varied. The shear-induced segregation force is found to be proportional to the shear rate gradient, which effectively pushes the large intruder from lower to higher shear rate regions. A scaling law is developed for the segregation force that is accurate over a wide range of overburden pressures and shear rates, and hence inertial numbers.

Growth of the microfluidics field has triggered numerous advances in focusing and separating microparticles, with such systems rapidly finding applications in biomedical, chemical, and environmental fields. The use of shear-thinning viscoelastic fluids in microfluidic channels is leading to evolution of elasto-inertial focusing. Herein, we showed that the interplay between the elastic and shear-gradient lift forces, as well as the secondary flow transversal drag force that is caused by the non-zero second normal stress difference, lead to different particle focusing patterns in the elasto-inertial regime. Experiments and 3D simulations were performed to study the effects of flowrate, particle size, and the shear-thinning extent of the fluid on the focusing patterns. The Giesekus constitutive equation was used in the simulations to capture the shear-thinning and viscoelastic behaviors of the solution used in the experiments. At low flowrate, with Weissenberg number Wi ~ O(1), both the elastic force and secondary flow effects push particles towards the channel center. However, at a high flowrate, Wi ~ O(10), the elastic force direction is reversed in the central regions. This remarkable behavior of the elastic force, combined with the enhanced shear-gradient lift at the high flowrate, pushes particles away from the channel center. Additionally, a precise prediction of the focusing position can only be made when the shear-thinning extent of the fluid is correctly estimated in the modeling. The shear-thinning also gives rise to the unique behavior of the inertial forces near the channel walls which is linked with the ‘warped’ velocity profile in such fluids.

Al Barwani, Mohsin; Park, Jae Sung(
, Proceedings of the ASME 2022 International Mechanical Engineering Congress and Exposition)

The transition from laminar to turbulent flow is of great interest since it is one of the most difficult and unsolved problems in fluids engineering. The transition processes are significantly important because the transition has a huge impact on almost all systems that come in contact with a fluid flow by altering the mixing, transport, and drag properties of fluids even in simple pipe and channel flows. Generally, in most transportation systems, the transition to turbulence causes a significant increase in drag force, energy consumption, and, therefore, operating cost. Thus, understanding the underlying mechanisms of the laminar-to-turbulent transition can be a major benefit in many ways, especially economically. There have been substantial previous studies that focused on testing the stability of laminar flow and finding the critical amplitudes of disturbances necessary to trigger the transition in various wall-bounded systems, including circular pipes and square ducts. However, there is still no fundamental theory of transition to predict the onset of turbulence. In this study, we perform direct numerical simulations (DNS) of the transition flows from laminar to turbulence in a channel flow. Specifically, the effects of different magnitudes of perturbations on the onset of turbulence are investigated. The perturbation magnitudes vary from 0.001 (0.1%) to 0.05 (5%) of a typical turbulent velocity field, and the Reynolds number is from 5,000 to 40,000. Most importantly, the transition behavior in this study was found to be in good agreement with other reported studies performed for fluid flow in pipes and ducts. With the DNS results, a finite amplitude stability curve was obtained. The critical magnitude of perturbation required to cause transition was observed to be inversely proportional to the Reynolds number for the magnitude from 0.01 to 0.05. We also investigated the temporal behavior of the transition process, and it was found that the transition time or the time required to begin the transition process is inversely correlated with the Reynolds number only for the magnitude from 0.02 to 0.05, while different temporal behavior occurs for smaller perturbation magnitudes. In addition to the transition time, the transition dynamics were investigated by observing the time series of wall shear stress. At the onset of transition, the shear stress experiences an overshoot, then decreases toward sustained turbulence. As expected, the average values of the wall shear stress in turbulent flow increase with the Reynolds number. The change in the wall shear stress from laminar to overshoot was, of course, found to increase with the Reynolds number. More interestingly was the observed change in wall shear stress from the overshoot to turbulence. The change in magnitude appears to be almost insensitive to the Reynolds number and the perturbation magnitude. Because the change in wall shear stress is directly proportional to the pumping power, these observations could be extremely useful when determining the required pumping power in certain flow conditions. Furthermore, the stability curve and wall shear stress changes can be considered robust features for future applications, and ultimately interpreted as evidence of progress toward solving the unresolved fluids engineering problem.

A numerical investigation of an asymptotically reduced model for quasigeostrophic
Rayleigh-Bénard convection is conducted in which the depth-averaged flows are numerically suppressed by modifying the governing equations. At the largest accessible values
of the Rayleigh number Ra, the Reynolds number and Nusselt number show evidence
of approaching the diffusion-free scalings of Re ∼ RaE/Pr and Nu ∼ Pr−1/2Ra3/2E2,
respectively, where E is the Ekman number and Pr is the Prandtl number. For large
Ra, the presence of depth-invariant flows, such as large-scale vortices, yield heat and
momentum transport scalings that exceed those of the diffusion-free scaling laws. The
Taylor microscale does not vary significantly with increasing Ra, whereas the integral
length scale grows weakly. The computed length scales remain O(1) with respect to the
linearly unstable critical wave number; we therefore conclude that these scales remain
viscously controlled. We do not find a point-wise Coriolis-inertia-Archimedean (CIA)
force balance in the turbulent regime; interior dynamics are instead dominated by horizontal advection (inertia), vortex stretching (Coriolis) and the vertical pressure gradient. A
secondary, subdominant balance between the Archimedean buoyancy force and the viscous
force occurs in the interior and the ratio of the root mean square (rms) of these two forces
is found to approach unity with increasing Ra. This secondary balance is attributed to
the turbulent fluid interior acting as the dominant control on the heat transport. These
findings indicate that a pointwise CIA balance does not occur in the high Rayleigh number
regime of quasigeostrophic convection in the plane layer geometry. Instead, simulations
are characterized by what may be termed a nonlocal CIA balance in which the buoyancy
force is dominant within the thermal boundary layers and is spatially separated from the
interior Coriolis and inertial forces.

Jing, Lu, Ottino, Julio M., Umbanhowar, Paul B., and Lueptow, Richard M. Drag force in granular shear flows: regimes, scaling laws and implications for segregation. Retrieved from https://par.nsf.gov/biblio/10358658. Journal of Fluid Mechanics 948. Web. doi:10.1017/jfm.2022.706.

Jing, Lu, Ottino, Julio M., Umbanhowar, Paul B., & Lueptow, Richard M. Drag force in granular shear flows: regimes, scaling laws and implications for segregation. Journal of Fluid Mechanics, 948 (). Retrieved from https://par.nsf.gov/biblio/10358658. https://doi.org/10.1017/jfm.2022.706

Jing, Lu, Ottino, Julio M., Umbanhowar, Paul B., and Lueptow, Richard M.
"Drag force in granular shear flows: regimes, scaling laws and implications for segregation". Journal of Fluid Mechanics 948 (). Country unknown/Code not available. https://doi.org/10.1017/jfm.2022.706.https://par.nsf.gov/biblio/10358658.

@article{osti_10358658,
place = {Country unknown/Code not available},
title = {Drag force in granular shear flows: regimes, scaling laws and implications for segregation},
url = {https://par.nsf.gov/biblio/10358658},
DOI = {10.1017/jfm.2022.706},
abstractNote = {The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations.},
journal = {Journal of Fluid Mechanics},
volume = {948},
author = {Jing, Lu and Ottino, Julio M. and Umbanhowar, Paul B. and Lueptow, Richard M.},
}

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