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ON THE DRAG COEFFICIENT OF NON-SPHERICAL PARTICLES Gholamhossein Bagheri1
Costanza Bonadonna1 Irene Manzella1 Piero Pontelandolfo2
Pierre Vonlanthen3 Patrick Haas2 1Section of Earth Science, University of Geneva, Switzerland 2hepia/CMEFE, Geneva, Switzerland 3Institut des sciences de la Terre, Lausanne, 1015, Switzerland
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Outline
Introduction
objectives Methodology
Analytical solutions (Re << 1)
Settling columns (10 < Re < 103)
Vertical wind tunnel (103 < Re < 105)
Results
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Particle size and shape The most important factors to determine particle velocity and its atmospheric residence time
Particle terminal velocity can be evaluated if its drag coefficient (CD) is known
Introduction
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Objectives Effect of particle shape and surface vesicularity on the drag force?
Benchmarking existing models and shape descriptors
Presenting a new model based on easy-to-measure shape descriptors
Introduction
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Sphere drag
Methodology
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Approaching the problem
Methodology
CD of any arbitrary shape particle at intermediate Re is a function of its CD at very low Re and very high Re
Re<<1
1000<Re<3×105
1<Re<1000
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Approaching the problem
Methodology
In other words: CD=f (Re, K1, K2) where K1 and K2 are functions of particles shape
K1=CD/CD,Sphere
K2=CD/CD,Sphere
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Approaching the problem
Methodology
In other words: CD=f (Re, K1, K2) where K1 and K2 are functions of particles shape
K1 = CD / CD,Sphere
K2 = CD / CD,Sphere
CD =24K1Re
(1+0.15(ReK2 / K1)0.687 )+
0.46K2
1+ 42500(ReK2 / K1)
1.16
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Approaching the problem
Methodology
Analytical solution
Wind tunnel
settling columns
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Re<<1
Methodology
Analytical solution exists only for sphere and ellipsoid
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10<Re <103
Methodology
Experiments in settling columns 117 particles (100 volcanic), 150 µm< diameter< 1 mm 3.6 m
0.45 m
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Particle Characterization
Samples: Settling columns
117 particles (100 volcanic)
150 µm < diameter< 1 mm
SEM micro-CT and Image analysis
Bagheri et al., Powder Technology (2014), 270(A)
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104<Re <105
Methodology
Experiments in vertical wind tunnel 177 particles (116 volcanic), 11 mm< diameter< 36 mm
Bagheri et al., Rev. Sci. Instrum. (2013), 84 (5)
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Particle Characterization
Samples: Settling columns
177 particles (116 volcanic)
11 mm < diameter < 36 mm
3D laser scan and Image analysis
Bagheri et al., Powder Technology (2014), 270(A)
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Why vertical wind tunnel?
Methodology
Falling columns: A spherical particle with
diameter of 2 cm and density of 2700 kgm-3
Air (density ratio = 2700) Water (density ratio = 2.7)
324 m
0.5 m
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Particle secondary motion
Bagheri et al., Rev. Sci. Instrum. (2013), 84 (5)
100 cm
25 frame per second
Methodology: The vertical Wind tunnel
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Particle secondary motion
Methodology: The vertical Wind tunnel
Bagheri et al., Rev. Sci. Instrum. (2013), 84 (5)
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Particle secondary motion
Methodology: The vertical Wind tunnel
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Wind Tunnel setup
Bagheri et al., Rev. Sci. Instrum. (2013), 84 (5)
Methodology: The vertical Wind tunnel
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Particle tracking code
d = 2 cm L = 4.7 cm m = 9.3 gr
L
d
Bagheri et al., Rev. Sci. Instrum. (2013), 84 (5)
Methodology
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Which shape descriptor correlates with K1?
Results C
D /
CD
, Sph
ere
=K1
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Which shape descriptor correlates with K1?
Results C
D /
CD
, Sph
ere
=K1
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Results C
D /
CD
, Sph
ere
=K1
Which shape descriptor correlates better with K1?
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Surface roughness effects at Re<<1
Hill & Power theorem (1956):
Results
CD / CD, Sphere=1.04
CD / CD, Sphere=1.07
CD / CD, Sphere≈1.05
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Which shape descriptor correlates with K2?
Results C
D =
0.4
63×K
2
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Which shape descriptor correlates with K2?
Results C
D =
0.4
63×K
2
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Results C
D =
0.4
63×K
2
Which shape descriptor correlates better with K2?
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Surface roughness effect at high Re At least at high Re the effect of surface roughness is almost negligible
(< 7 %)
Rough: Without Parafilm wrap
Smooth: With Parafilm wrap
Results
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New model of CD
Results
K1 = f ( )
K2 = g ( )
S I L
S 3 I L2
CD =24K1Re
(1+0.15(ReK2 / K1)0.687 )+
0.46K2
1+ 42500(ReK2 / K1)
1.16
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New model of CD
Results
K1 = f ( )
K2 = g ( )
S I L
S 3 I L2
CD =24K1Re
(1+0.15(ReK2 / K1)0.687 )+
0.46K2
1+ 42500(ReK2 / K1)
1.16
3.6 m
0.45 m
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Intermediate Re: estimations vs. measurements
Results
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Intermediate Re: estimations vs. measurements
Results
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Intermediate Re: estimations vs. measurements
Results
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First model of drag coefficient for freely moving non-spherical
particles in air
Ø Valid in a wide range of Reynolds number (Re<105)
Ø Valid for spherical, regular and irregular particles
Ø Easy-to-measure shape factors (for low and high Re)
Ø Lowest value of estimation error and uncertainty
New drag coefficient model
Conclusions