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Experimental Study of Particle Settling Velocities Corrine Jacobs, Marek Jendrassak, Roi Gurka and Erin Hackett
Stokes Number
Results
References:
Experiment
Conclusions
𝜏𝑝 =𝜌𝑝 𝑑50
2
18𝜇
Acknowledgments:
Particles
Oscillating grid facility generating homogenous turbulence
Vortex trapping / acceleration model Kawanisi and Shiozaki (2008)
Turbulent properties calculated 15 cm below the grid
v’rms increases with grid frequency
Well mixed homogeneous flow conditions
Distribution of particles diameter - d50
Shape
The reduction model: Particle gets ‘trapped’ in the vortex of fluid reducing the settling velocity (Magelli et. al., 1990)
The enhancement model: Particle aligns in the downward sections of each eddy in the flow increasing the settling velocity (Aliseda et. al., 2002)
Particle - turbulence interactions impact relative proportion of enhancement and reduction of settling velocities (Doroodchi et. al., 2008)
Settling velocity is affected by turbulence through the drag force
100 µm 500 µm
Natural sand Synthetic particles
Flow Field Analysis
Particle Tracking Analysis
Particle Image velocimetry (PIV): Nd:YAG dual head Laser CCD double exposure camera Synchronizer
Particle tracking: Monochrome LED light (green) CMOS high speed camera
Grid Turbulence: Stroke: 0 - 100 mm Frequency: 2 - 7 Hz Grid: 31.5 mm mesh size
Aliseda, A., A. Cartellier, F. Hainaux, and J.C. Lasheras (2002) “Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence” J. Fluid Mech. vol. 468, pp. 77 DOI: 10.1017/S0022112002001593 Doroodchi E., G.M. Evans, M.P. Schwarz, G.L. Lane, N. Shah, and A. Nguyen (2008) “Influence of turbulence intensity on particle drag coefficients” Chemical Engineering Journal vol.135 , pp. 129–134
Example of PIV velocity map
Instantaneous velocities used to compute turbulence statistics
500 vector maps were acquired for
each particle and grid frequency
Trajectories of individual particles
Blob analysis used to identify and track individual particles – 4000 2D trajectories
Horizontal and vertical velocities obtained from
trajectories using Lagrangian approach
Histogram of particle’s settling velocity
2000 sample points of vertical velocities obtained for each particle type and frequency
V - Settling velocity - mean of vertical velocities
σ - Variability of vertical (settling) velocities
Particles show either no change or an enhancement of settling velocity. Enhancement in settling velocity is largest for particles with smallest Stokes Numbers. Particles with large Stokes Numbers are least influenced by turbulence. Particles in the middle range show a polynomial dependence on Stokes Number. Particles with Stokes Numbers ~10-3 show the largest change in settling velocity. Settling velocity variability increases as the Stokes Number decreases.
Particle type Natural
sand Industrial
sand 1 Industrial
sand 2 Industrial
sand 3 Synthetic
Density (𝒈
𝒄𝒄) 1.65 2.64 3.97 2.20 1.44
d50 (µm) 1400, 621, 261, 146
990, 831, 291
147, 109 95 97, 71
𝜏𝑓 =𝐿𝑒
𝑣′𝑟𝑚𝑠
Stokes Number (St) = 𝝉𝒑
Particle relaxation time
Fluid turnover time
V’rms (cm/s)
Ver
tica
l dir
ecti
on
(cm
)
Integral length scale - 𝐿𝑒
0.04 0.09 0.14 x (m)
Freq
uen
cy
Vertical Velocity (cm/s)
V = -9.2 cm/s σ = 2.2 cm/s
We would like to thank W. Merchant and Dr. V. Limpasuvan for their help with the tracking algorithms as well as the II-VI Foundation for their support of this research.
Laser Diffraction Particle Size Analyzer:
Settling velocity enhanced due to
turbulence
Settling velocity in still and turbulent water Empirical
curves for stagnant flow
(Dietrich, 1982)
Variability of settling velocity
Settling velocity
Settling velocity can be either increased or reduced:
Introduction
Reduction Enhancement
Combination
Small St Middle St Large St
𝝉𝒇
𝐿𝑒
Grid frequency
Grid frequency
3 Hz Natural Sand 620 mm
[email protected] Magelli, F., D. Fajner, M. Nocentini, and G. Pasquali (1990) “Solid distribution in vessels stirred with multiple impellers” Chemical engineering science, vol 45, pp. 615-625 Kawanisi, K. and R. Shiozaki (2008) ”Turbulent Effects on the Settling Velocity of Suspended Sediment” J. Hydraul. Eng., vol 134, pp. 261–266 , DOI: 10.1061/(ASCE)0733-9429(2008)134:2(261) Dietrich W. (1982) “Settling Velocity of Natural Particles” Water Resources Research vol 18, pp. 1615-1626
Particle diameter (µm)
08/23/2014
