| 1. |
- Cabrera, F., et al.
(författare)
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Experimental validation of fluid inertia models for a cylinder settling in a quiescent flow
- 2022
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Ingår i: Physical Review Fluids. - 2469-990X. ; 7:2
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Tidskriftsartikel (refereegranskat)abstract
- The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds number. In our experiments, we can, to a very good approximation, relate the rate of rotation of cylindrical tungsten rods, of aspect ratios = 8 and = 16, settling in pure glycerol, to the torque they are experiencing. This allows us to compare the measured torque with expressions obtained either in the slender-rod limit or in the case of spheroids. Both theories predict a simple angle dependence for the torque, which is found to capture very well the experimental results. The slender-rod theory overestimates the results for the two aspect ratios considered, while the expression obtained for a spheroid provides a better approximation for = 16. Comparing our results with those of previous experiments provides further insight on the conditions of validity of the slender-rod theory. The translational dynamics is shown to be in qualitative agreement with the slender-rod and spheroid models, the former one being found to represent better the experimental data.
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| 2. |
- Gustavsson, Kristian, 1980, et al.
(författare)
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Effect of fluid inertia on the orientation of a small prolate spheroid settling in turbulence
- 2019
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Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 21
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Tidskriftsartikel (refereegranskat)abstract
- We study the angular dynamics of small non-spherical particles settling in a turbulent flow, such as ice crystals in clouds, aggregates of organic material in the oceans, or fibres settling in turbulent pipe flow. Most solid particles encountered in Nature are not spherical, and their orientations affect their settling speeds, as well as their collision and aggregation rates in suspensions. Whereas the random action of turbulent eddies favours an isotropic distribution of orientations, gravitational settling breaks the rotational symmetry. The precise nature of the symmetry breaking, however, is subtle. We demonstrate here that the fluid-inertia torque plays a dominant role in the problem. As a consequence rod-like particles tend to settle in turbulence with horizontal orientation, the more so the larger the settling number Sv (a dimensionless measure of the settling speed). For large Sv we determine the fluctuations around this preferential horizontal orientation for prolate particles with arbitrary aspect ratios, assuming small Stokes number St (a dimensionless measure of particle inertia). Our theory is based on a statistical model representing the turbulent velocity fluctuations by Gaussian random functions. This overdamped theory predicts that the orientation distribution is very narrow at large Sv, with a variance proportional to Sv(-4). By considering the role of particle inertia, we analyse the limitations of the overdamped theory, and determine its range of applicability. Our predictions are in excellent agreement with numerical simulations of simplified models of turbulent flows. Finally we contrast our results with those of an alternative theory predicting that the orientation variance is proportional to Sv(-2) at large Sv.
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| 3. |
- Gustavsson, Kristian, 1980, et al.
(författare)
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Effect of Particle Inertia on the Alignment of Small Ice Crystals in Turbulent Clouds
- 2021
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Ingår i: Journal of the Atmospheric Sciences. - : American Meteorological Society. - 0022-4928 .- 1520-0469. ; 78:8, s. 2573-2587
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Tidskriftsartikel (refereegranskat)abstract
- Small nonspherical particles settling in a quiescent fluid tend to orient so that their broad side faces down because this is a stable fixed point of their angular dynamics at small particle Reynolds number. Turbulence randomizes the orientations to some extent, and this affects the reflection patterns of polarized light from turbulent clouds containing ice crystals. An overdamped theory predicts that turbulence-induced fluctuations of the orientation are very small when the settling number Sv (a dimensionless measure of the settling speed) is large. At small Sv, by contrast, the overdamped theory predicts that turbulence randomizes the orientations. This overdamped theory neglects the effect of particle inertia. Therefore, we consider here how particle inertia affects the orientation of small crystals settling in turbulent air. We find that it can significantly increase the orientation variance, even when the Stokes number St (a dimensionless measure of particle inertia) is quite small. We identify different asymptotic parameter regimes where the tilt-angle variance is proportional to different inverse powers of Sv. We estimate parameter values for ice crystals in turbulent clouds and show that they cover several of the identified regimes. The theory predicts how the degree of alignment depends on particle size, shape, and turbulence intensity, and that the strong horizontal alignment of small crystals is only possible when the turbulent energy dissipation is weak, on the order of 1 cm(2) s(-3) or less.
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| 4. |
- Gustavsson, Kristian, 1980, et al.
(författare)
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Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence
- 2017
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 119
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Tidskriftsartikel (refereegranskat)abstract
- The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.
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| 5. |
- Sheikh, M. Z., et al.
(författare)
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Colliding Ice Crystals in Turbulent Clouds
- 2022
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Ingår i: Journal of the Atmospheric Sciences. - : American Meteorological Society. - 0022-4928 .- 1520-0469. ; 79:9, s. 2205-2218
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Tidskriftsartikel (refereegranskat)abstract
- Collisions, resulting in aggregation of ice crystals in clouds, is an important step in the formation of snow aggregates. Here, we study the collision process by simulating spheroid-shaped particles settling in turbulent flows and by determining the probability of collision. We focus on platelike ice crystals (oblate ellipsoids), subject to gravity, and to the Stokes force and torque generated by the surrounding fluid. We also take into account the contributions to the drag and torque due to fluid inertia, which are essential to understand the tendency of crystals to settle with their largest dimension oriented horizontally. We determine the collision rate between identical crystals, of diameter 300 mu m, with aspect ratios in the range 0.005 <=-beta <=-0.05, and over a range of energy dissipation per unit mass, epsilon, 1 <=-epsilon <=-250 cm(2 )s(-3). For all values of beta studied, the collision rate increases with the turbulence intensity. The dependence on beta is more subtle. Increasing beta at low turbulence intensity (epsilon <= 16 cm(2) s(-3)) diminishes the collision rate, but increases it at higher epsilon asymptotic to 250 cm(2) s(-3). The observed behaviors can be understood as resulting from three main physical effects. First, the velocity gradients in a turbulent flow tend to bring particles together. In addition, differential settling plays a role at small epsilon when the particles are thin enough (beta small), whereas the prevalence of particle inertia at higher epsilon leads to a strong enhancement of the collision rate.
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| 6. |
- Sheikh, M. Z., et al.
(författare)
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Effect of Turbulence on the Collision Rate between Settling Ice Crystals and Droplets
- 2024
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Ingår i: JOURNAL OF THE ATMOSPHERIC SCIENCES. - 0022-4928 .- 1520-0469. ; 81:5, s. 887-901
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Tidskriftsartikel (refereegranskat)abstract
- In mixed -phase clouds, graupel forms by riming, a process whereby ice crystals and supercooled water droplets settling through a turbulent fl ow collide and aggregate. We consider here the early stage of the collision process of small ice crystals with water droplets and determine numerically the geometric collision kernel in turbulent fl ows (therefore neglecting all interactions between the particles and assuming a collision ef fi ciency equal to unity), over a range of energy dissipation rate 1 - 250 cm 2 s 23 relevant to cloud microphysics. We take into account the effect of small, but nonzero fl uid inertia, which is essential since it favors a biased orientation of the crystals with their broad side down. Since water droplets and ice crystals have different masses and shapes, they generally settle with different velocities. Turbulence does not play any signi fi cant role on the collision kernel when the difference between the settling velocities of the two sets of particles is larger than a few millimeters per second. The situation is completely different when the settling speeds of droplets and crystals are comparable, in which case turbulence is the main cause of collisions. Our results are compatible with those of recent experiments according to which turbulence does not clearly increase the growth rate of tethered graupel in a fl ow transporting water droplets.
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| 7. |
- Sheikh, M. Z., et al.
(författare)
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Importance of fluid inertia for the orientation of spheroids settling in turbulent flow
- 2020
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 886
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Tidskriftsartikel (refereegranskat)abstract
- How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid that is set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent fluid-velocity gradients, on the other hand, tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inertia, but taking into account the effect of the turbulent fluid-velocity gradients on the particle orientation. These studies reached the opposite conclusion, namely that the particle tends to settle with its narrow edge first, therefore minimising the drag on the particle. Here, we consider both effects, the convective inertial torque as well as the torque due to fluctuating fluid-velocity gradients. We ask under which circumstances either one or the other dominates. To this end we estimate the ratio of the magnitudes of the two torques. Our estimates suggest that the fluid-inertia torque prevails in high-Reynolds-number flows. In this case non-spherical particles tend to settle with orientations maximising drag. But when the Reynolds number is small, then the torque due to fluid-velocity gradients may dominate, causing the particle to settle with its narrow edge first, minimising the drag.
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