On the drag of freely falling non-spherical particles

Bagheri, Gholamhossein; Bonadonna, Costanza

doi:10.1016/j.powtec.2016.06.015

Cited by 256 publications

(257 citation statements)

References 43 publications

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“…The correlation coefficient r is also reported. Pfeiffer et al (2005) 16.07% Ganser (1993) 14.49% Bagheri and Bonadonna (2016) 24.66% Dioguardi and Mele (2015) 13.49% This work (equation (14)) 12.76%…”

Section: 1002/2017jb014926mentioning

confidence: 84%

“…Ganser (1993) shows the opposite, the value of the slope being 0.95, which could be attributed to the tendency to overestimate the drag coefficient (=underestimation of terminal velocity) at very high Re that is not counter balanced by the evident tendency to overestimate the terminal velocity at very low Re. Bagheri and Bonadonna (2016) had the poorest performance after Dellino et al (2005), with a value of the slope of 1.261, meaning a general tendency to overestimate terminal velocities, which, in turn, is the result of the drag underestimation in the whole investigated Re range. Finally, Dioguardi and Mele (2015) and the new drag law ( (14) had the best performances, being a equal to 0.99 and 1, respectively.…”

Section: 1002/2017jb014926mentioning

confidence: 96%

“…Going deeper into detail, it can be seen that (14) further improved the performance at very low Re and in the range 10-100, which is the most problematic for Dioguardi and Mele (2015); this was not surprising, since this range includes the critical value Re = 50 at which there is the switch between the two parts of the law (see equation (19)). (2005), Ganser (1993), Bagheri and Bonadonna (2016), Dioguardi and Mele (2015), and (14).…”

Section: Dioguardi and Mele (2015)mentioning

confidence: 99%

“…Scatter log-log plots comparing the terminal velocity calculated with six selected drag laws w t,calc and the corresponding measured values for the particles in our database, w t,meas . The drag laws are Dellino et al (2005), Pfeiffer et al (2005), Ganser (1993), Bagheri and Bonadonna (2016), Dioguardi and Mele (2015), and (14). The solid black line is the best fit line of type y = ax.…”

Section: 1002/2017jb014926mentioning

confidence: 99%

“…AERODYNAMIC DRAG OF IRREGULAR PARTICLES 144 Zhu et al, 2017), pyroclastic flows (e.g., Dellino et al, 2008;, eruptive columns (e.g., Cerminara et al, 2016;Folch et al, 2016), and distal ash clouds (e.g., Beckett et al, 2015;Bonadonna et al, 2012;Bonasia et al, 2010;Costa et al, 2012Costa et al, , 2006). Therefore, a major effort has been posed to find reliable shapedependent drag laws that work on the widest possible range of fluid dynamic regimes quantified by Re (Alfano et al, 2011;Bagheri & Bonadonna, 2016;Chhabra et al, 1999;Chien, 1994;Dellino et al, 2005;Dioguardi et al, 2017;Dioguardi & Mele, 2015;Ganser, 1993;Haider & Levenspiel, 1989;Hölzer & Sommerfeld, 2008;Loth, 2008;Pfeiffer et al, 2005;Swamee & Ojha, 1991;Tran-Cong et al, 2004;Wilson & Huang, 1979). These drag laws are a function of different shape descriptors, among which sphericity Φ is the most widely used.…”

Section: Introductionmentioning

confidence: 99%

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A New One‐Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number

2018

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A new drag law for irregularly shaped particles is presented here. Particles are described by a shape factor that takes into account both sphericity and circularity, which can be measured via the most commonly used image particle analysis techniques. By means of the correlation of the drag coefficient versus the particle Reynolds number and the shape factor, a new drag formula, which is valid over a wide range of Reynolds number (0.03–10,000), is obtained. The new model is able to reproduce the drag coefficient of particles measured in terminal velocity experiments with a smaller scatter compared to other laws commonly used in multiphase flow engineering and volcanology. Furthermore, the new formula uses only one equation, whereas previous models, to insure validity over an ample range, made use of a step function that introduces a discontinuity at the switch of equations. Finally, this drag law works in the whole range of variation, from extremely irregular particles to perfect sphere. A code of the iterative algorithm for the drag coefficient calculation and terminal velocity is included in the supporting information both as a Fortran routine and a Matlab function.

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Section: 1002/2017jb014926mentioning

confidence: 84%

Section: 1002/2017jb014926mentioning

confidence: 96%

Section: Dioguardi and Mele (2015)mentioning

confidence: 99%

Section: 1002/2017jb014926mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New One‐Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number

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Reference data set of volcanic ash physicochemical and optical properties

et al. 2017

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Uncertainty in the physicochemical and optical properties of volcanic ash particles creates errors in the detection and modeling of volcanic ash clouds and in quantification of their potential impacts. In this study, we provide a data set that describes the physicochemical and optical properties of a representative selection of volcanic ash samples from nine different volcanic eruptions covering a wide range of silica contents (50–80 wt % SiO2). We measured and calculated parameters describing the physical (size distribution, complex shape, and dense‐rock equivalent mass density), chemical (bulk and surface composition), and optical (complex refractive index from ultraviolet to near‐infrared wavelengths) properties of the volcanic ash and classified the samples according to their SiO2 and total alkali contents into the common igneous rock types basalt to rhyolite. We found that the mass density ranges between ρ = 2.49 and 2.98 g/cm3 for rhyolitic to basaltic ash types and that the particle shape varies with changing particle size (d < 100 μm). The complex refractive indices in the wavelength range between λ = 300 nm and 1500 nm depend systematically on the composition of the samples. The real part values vary from n = 1.38 to 1.66 depending on ash type and wavelength and the imaginary part values from k = 0.00027 to 0.00268. We place our results into the context of existing data and thus provide a comprehensive data set that can be used for future and historic eruptions, when only basic information about the magma type producing the ash is known.

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In‐flight dynamics of volcanic ballistic projectiles

Taddeucci

Alatorre‐Ibargüengoitia

Cruz-Vázquez

et al. 2017

Reviews of Geophysics

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Centimeter to meter‐sized volcanic ballistic projectiles from explosive eruptions jeopardize people and properties kilometers from the volcano, but they also provide information about the past eruptions. Traditionally, projectile trajectory is modeled using simplified ballistic theory, accounting for gravity and drag forces only and assuming simply shaped projectiles free moving through air. Recently, collisions between projectiles and interactions with plumes are starting to be considered. Besides theory, experimental studies and field mapping have so far dominated volcanic projectile research, with only limited observations. High‐speed, high‐definition imaging now offers a new spatial and temporal scale of observation that we use to illuminate projectile dynamics. In‐flight collisions commonly affect the size, shape, trajectory, and rotation of projectiles according to both projectile nature (ductile bomb versus brittle block) and the location and timing of collisions. These, in turn, are controlled by ejection pulses occurring at the vent. In‐flight tearing and fragmentation characterize large bombs, which often break on landing, both factors concurring to decrease the average grain size of the resulting deposits. Complex rotation and spinning are ubiquitous features of projectiles, and the related Magnus effect may deviate projectile trajectory by tens of degrees. A new relationship is derived, linking projectile velocity and size with the size of the resulting impact crater. Finally, apparent drag coefficient values, obtained for selected projectiles, mostly range from 1 to 7, higher than expected, reflecting complex projectile dynamics. These new perspectives will impact projectile hazard mitigation and the interpretation of projectile deposits from past eruptions, both on Earth and on other planets.

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On the drag of freely falling non-spherical particles

Cited by 256 publications

References 43 publications

A New One‐Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number

A New One‐Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number

Reference data set of volcanic ash physicochemical and optical properties

In‐flight dynamics of volcanic ballistic projectiles

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