scholarly journals Effect of particle inertia on the alignment of small ice crystals in turbulent clouds

2021 ◽  
Author(s):  
K. Gustavsson ◽  
M. Z. Sheikh ◽  
A. Naso ◽  
A. Pumir ◽  
B. Mehlig
Keyword(s):  
Turbulent Energy ◽  
Stokes Number ◽  
Ice Crystals ◽  
Spherical Particles ◽  
Particle Inertia ◽  
Small Crystals ◽  
Asymptotic Parameter ◽  
Settling Speed ◽  
Parameter Values ◽  
Quiescent Fluid

AbstractSmall non-spherical 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 randomises the orientations to some extent, and this affects the reflection patterns of polarised 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 randomises 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, of the order of 1cm2/s3 or less.

Mapping spheroid rotation modes in turbulent channel flow: effects of shear, turbulence and particle inertia

2019 ◽  
Vol 876 ◽  
pp. 19-54 ◽  
Author(s):  
Lihao Zhao ◽  
Niranjan R. Challabotla ◽  
Helge I. Andersson ◽  
Evan A. Variano
Keyword(s):  
Channel Flow ◽  
Time Scale ◽  
Turbulent Channel Flow ◽  
Stokes Number ◽  
Particle Orientation ◽  
Spherical Particles ◽  
Rotational Behaviour ◽  
Particle Rotation ◽  
Particle Inertia ◽  
Buffer Region

The rotational behaviour of non-spherical particles in turbulent channel flow is studied by Lagrangian tracking of spheroidal point particles in a directly simulated flow. The focus is on the complex rotation modes of the spheroidal particles, in which the back reaction on the flow field is ignored. This study is a sequel to the letter by Zhao et al. (Phys. Rev. Lett., vol. 115, 2015, 244501), in which only selected results in the near-wall buffer region and the almost-isotropic channel centre were presented. Now, particle dynamics all across the channel is explored to provide a complete picture of the orientational and rotational behaviour with consideration of the effects of particle aspect ratio ranging from 0.1 to 10 and particle Stokes number from 0 (inertialess) to 30. The rotational dynamics in the innermost part of the logarithmic wall layer is particularly complex and affected not only by modest mean shear, but also by particle inertia and turbulent vorticity. While inertial disks exhibit modest preferential orientation in either the wall-normal or cross-stream direction, inertial rods show neither preferential tumbling nor spinning. Examination of the co-variances between particle orientation, particle rotation and fluid rotation vectors explains the qualitatively different ‘wall mode’ rotation and ‘centre mode’ rotation. Inertialess spheroids transition between the two modes within a narrow zone ($15<z^{+}<35$) in the buffer region. If the spheroids have inertia, the transition zone between the two modes shifts to the inner part of the logarithmic layer, i.e. $z^{+}\geqslant 40$. We ascribe the transition of inertialess spheroids from the ‘wall mode’ to the ‘centre mode’ rotation to the changeover between the time scales associated with mean shear and small-scale turbulence. Inertial spheroids, however, transition between the two rotational modes when the Kolmogorov time scale becomes comparable to the time scale for particle rotation, i.e. the effective Stokes number is of order unity. The aforementioned findings reveal, in addition to the effects of particle shape and alignment, the importance of the characteristic local time scale of fluid flow for the rotation of both tracer and inertial spheroids in turbulent channel flows.

scholarly journals Sedimentation of finite-size spheres in quiescent and turbulent environments

2016 ◽  
Vol 788 ◽  
pp. 640-669 ◽  
Author(s):  
Walter Fornari ◽  
Francesco Picano ◽  
Luca Brandt
Keyword(s):  
Turbulent Flow ◽  
Settling Velocity ◽  
Solid Phase ◽  
Density Ratio ◽  
Finite Size ◽  
Spherical Particles ◽  
Volume Fractions ◽  
Turbulent Environments ◽  
The Mean ◽  
Quiescent Fluid

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

Transport of Non-Spherical Particles in Turbulence: Application of the LBM

2006 ◽  
Author(s):  
Andreas Ho¨lzer ◽  
Martin Sommerfeld
Keyword(s):  
Angular Velocity ◽  
Turbulent Flow ◽  
Radial Direction ◽  
Stokes Number ◽  
Spherical Particles ◽  
Axis Ratio ◽  
Angular Velocities ◽  
Boltzmann Method ◽  
Short Time ◽  
Cylindrical Particles

Direct numerical simulations of the motion of volume equivalent single cylindrical particles with axis ratios of 1, 2, 3, and 4 and Stokes numbers of 1, 2, 4, and 40 in a homogeneous isotropic turbulent flow field are presented. The forced turbulent flow is simulated using the Lattice Boltzmann Method (LBM). It is observed that the rms velocity and the rms angular velocity in longitudinal and in radial direction are identical for every particle, even though the rms forces can differ more than 100% and the rms torque more than 1000% in both directions. However, these differences in force and torque result in a different short-time behaviour of the particle in longitudinal and in radial direction. The rms particle velocity is found to decrease with increasing axis ratio and the rms particle angular velocity to have a maximum at an axis ratio of about 2.5. The ratio of the rms velocity of the particle to that of the fluid decreases with increasing Stokes number as well as the ratio between the rms angular velocities, as one could expect.

Effect of microstructural anisotropy on the fluid–particle drag force and the stability of the uniformly fluidized state

2012 ◽  
Vol 713 ◽  
pp. 27-49 ◽  
Author(s):  
William Holloway ◽  
Jin Sun ◽  
Sankaran Sundaresan
Keyword(s):  
Friction Coefficient ◽  
Drag Force ◽  
Fluid Model ◽  
Stokes Number ◽  
Spherical Particles ◽  
Force Model ◽  
Drag Model ◽  
Fluidized State ◽  
Two Fluid Model ◽  
Two Fluid

AbstractLattice-Boltzmann simulations of fluid flow through sheared assemblies of monodisperse spherical particles have been performed. The friction coefficient tensor extracted from these simulations is found to become progressively more anisotropic with increasing Péclet number, $Pe= \dot {\gamma } {d}^{2} / D$, where $\dot {\gamma } $ is the shear rate, $d$ is the particle diameter, and $D$ is the particle self-diffusivity. A model is presented for the anisotropic friction coefficient, and the model constants are related to changes in the particle microstructure. Linear stability analysis of the two-fluid model equations including the anisotropic drag force model developed in the present study reveals that the uniformly fluidized state of low Reynolds number suspensions is most unstable to mixed mode disturbances that take the form of vertically travelling waves having both vertical and transverse structures. As the Stokes number increases, the transverse-to-vertical wavenumber ratio decreases towards zero; i.e. the transverse structure becomes progressively less prominent. Fully nonlinear two-fluid model simulations of moderate to high Stokes number suspensions reveal that the anisotropic drag model leads to coarser gas–particle flow structures than the isotropic drag model.

Scaling Laws for Metering the Flow of Gas-Particle Suspensions Through Venturis

1982 ◽  
Vol 104 (1) ◽  
pp. 88-91 ◽  
Author(s):  
J. Lee ◽  
C. T. Crowe
Keyword(s):  
Pressure Drop ◽  
Scaling Laws ◽  
Stokes Number ◽  
Spherical Particles ◽  
Dimensional Model ◽  
Particle Suspensions ◽  
One Dimensional ◽  
Coal Particles ◽  
Scaling Parameters ◽  
Loading Ratio

An experimental investigation was undertaken to determine those scaling parameters applicable to measuring the mass flow rate of gas-particle suspensions through venturis. It was found that Stokes number and the particle/gas loading ratio are the two most important parameters. The results show that pressure drop increases linearly with loading ratio and decreases monotonically with increasing Stokes number. The results also indicate that β-ratio and orientation of venturi do not significantly affect the pressure drop. Data for irregularly shaped pulverized coal particles show higher pressure drop compared with those for spherical particles. A quasi one-dimensional numerical model overpredicts the pressure drop, but a two-dimensional model demonstrates improved agreement.

scholarly journals Observations and modelling of microphysical variability, aggregation and sedimentation in tropical storm cirrus outflow regions

2011 ◽  
Vol 11 (8) ◽  
pp. 23761-23800
Author(s):  
M. W. Gallagher ◽  
P. J. Connolly ◽  
A. Heymsfield ◽  
K. N. Bower ◽  
T. W. Choularton ◽  
...  
Keyword(s):  
Collection Efficiency ◽  
Aerosol Particles ◽  
Tropical Storm ◽  
Cirrus Clouds ◽  
Ice Crystals ◽  
Aircraft Measurements ◽  
Ice Crystal ◽  
Crystal Aggregation ◽  
Small Crystals ◽  
Bulk Model

Abstract. Aircraft measurements of the microphysics of a tropical convective anvil (at temperatures ~−60 °C) forming above the HECTOR storm have been performed. The observed microphysics has been compared to a bulk and explicit microphysical model of the anvil region including crystal aggregation and sedimentation. It has been found that in flights made using straight and level runs perpendicular to the storm that the number of ice crystals initially decreased with distance from the storm as aggregation took place resulting in larger crystals followed by their loss due to sedimentation. At still greater distances from the storm the number of very small crystals increased. This is attributed to the formation of new ice crystals on aerosol particles as the ice super saturation rose following the depletion of the larger ice particles following aggregation and sedimentation. Comparison with the explicit microphysics model showed that the changes in the shapes of the ice crystal spectra as a function of distance from the storm could be explained by the explicit microphysical model if the aggregation efficiency was set to E~0.02. It is noteworthy that this aggregation efficiency is much larger than values normally used in cloud resolving models at these temperatures (typically E~0.0016). Furthermore if the bulk model is used then optimum agreement was reached with a collection efficiency for aggregation of E~0.05. These results are important for the treatment of the evolution and lifetime of tropical cirrus clouds.

scholarly journals Reduced particle settling speed in turbulence

2016 ◽  
Vol 808 ◽  
pp. 153-167 ◽  
Author(s):  
Walter Fornari ◽  
Francesco Picano ◽  
Gaetano Sardina ◽  
Luca Brandt
Keyword(s):  
Solid Phase ◽  
Density Ratio ◽  
Mean Square Displacement ◽  
Particle Diameter ◽  
Finite Size ◽  
Mean Square ◽  
Rigid Spheres ◽  
The Mean ◽  
Settling Speed ◽  
Quiescent Fluid

We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).

scholarly journals Topographically Generated Cloud Plumes

2006 ◽  
Vol 134 (8) ◽  
pp. 2108-2127 ◽  
Author(s):  
Qingfang Jiang ◽  
James D. Doyle
Keyword(s):  
Relative Humidity ◽  
Sierra Nevada ◽  
Rocky Mountain ◽  
Real Data ◽  
Ice Crystals ◽  
Small Crystals ◽  
Modis Image ◽  
Moderate Resolution ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
Moist Layer

Abstract Two topographically generated cirrus plume events have been examined through satellite observations and real-data simulations. On 30 October 2002, an approximately 70-km-wide cirrus plume, revealed by a high-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) image and a series of Geostationary Operational Environmental Satellite (GOES) images, originated from the Sierra Nevada ridge and extended northeastward for more than 400 km. On 5 December 2000, an approximately 400-km-wide cloud plume originated from the Southern Rocky Mountain massif and extended eastward for more than 500 km, the development of which was captured by a series of GOES images. The real-data simulations of the two cirrus plume events successfully capture the presence of these plumes and show reasonable agreement with the MODIS and GOES images in terms of the timing, location, orientation, length, and altitude of these cloud plumes. The synoptic and mesoscale aspects of the plume events, and the dynamics and microphysics relevant to the plume formation, have been discussed. Two common ingredients relevant to the cirrus plume formation have been identified, namely, a relatively deep moist layer aloft with high relative humidity and low temperature (≤−40°C near the cloud top), and strong updrafts over high terrain and slow descent downstream in the upper troposphere associated with terrain-induced inertia–gravity waves. The rapid increase of the relative humidity associated with strong updrafts creates a high number concentration of small ice crystals through homogeneous nucleation. The overpopulated ice crystals decrease the relative humidity, which, in return, inhibits small crystals from growing into large crystals. The small crystals with slow terminal velocities (&lt;0.2 m s−1) can be advected hundreds of kilometers before falling out of the moist layer.

scholarly journals Columnar structure formation of a dilute suspension of settling spherical particles in a quiescent fluid

2016 ◽  
Vol 1 (7) ◽  
Author(s):  
Sander G. Huisman ◽  
Thomas Barois ◽  
Mickaël Bourgoin ◽  
Agathe Chouippe ◽  
Todor Doychev ◽  
...  
Keyword(s):  
Structure Formation ◽  
Columnar Structure ◽  
Spherical Particles ◽  
Dilute Suspension ◽  
Quiescent Fluid

scholarly journals Observations of turbulence beneath sea ice in southern McMurdo Sound, Antarctica

2009 ◽  
Vol 6 (2) ◽  
pp. 1407-1436
Author(s):  
C. L. Stevens ◽  
N. J. Robinson ◽  
M. J. M. Williams ◽  
T. G. Haskell
Keyword(s):  
Sea Ice ◽  
Water Column ◽  
Unit Area ◽  
Supercooled Water ◽  
Turbulent Energy ◽  
Ice Crystals ◽  
Small Scale ◽  
Ice Shelf ◽  
Frazil Ice ◽  
Vertical Diffusivity

Abstract. The first turbulence profiler observations beneath land fast sea ice which is directly adjacent to an Antarctic ice shelf are described. The stratification in the 325 m deep water column consisted of a layer of supercooled water in the upper 40 m lying above a quasi-linearly stratified water column with a sharp step in density at mid-depth. Turbulent energy dissipation rates were on average 3×10−8 m2 s−3 with peak bin-averaged values reaching 4×10−7 m2 s−3. The local dissipation rate per unit area was estimated to be 10 mWm−2 on average with a peak of 50 mWm−2. These values are consistent with a moderate baroclinic response to the tides. The small-scale turbulent energetics lie on the boundary between isotropy and buoyancy-affected. This will likely influence the formation and aggregation of frazil ice crystals within the supercooled layer. An estimate of the vertical diffusivity of mass Kρ yields a coefficient of around 10−3 m2 s−1. Combining this estimate of Kρ with available observations of average and maximum currents suggests the layer of supercooled water can persist for a distance of ~20 km from the front of the McMurdo Ice Shelf.

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