Wall effects on the velocities of a single sphere settling in a stagnant and counter-current fluid and rising in a co-current fluid

Arsenijević, Zorana; Grbavčić, Željko; Garić‐Grulović, Radmila; Bošković‐Vragolović, Nevenka

doi:10.1016/j.powtec.2010.05.013

Cited by 32 publications

(12 citation statements)

References 35 publications

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“…3), and a 30 fps digital camcorder to record the path of the particle during its fall. Before starting the tests, it was found that the tube walls had no significant effect: using the expression proposed by Arsenijević et al (2010), the estimated error due to the wall effect, in the most unfavourable case, was less than 0.063%. The settling tube was filled with distilled water at 17 • C to keep the fluid parameters constant.…”

Section: Methodsmentioning

confidence: 99%

Simple settling velocity formula for calcareous sand

Alcerreca

Silva

Mendoza

2013

Journal of Hydraulic Research

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From the analysis of 1557 calcareous sand grains, a new equation for the computation of particle settling velocity is derived. The proposed expression involves only the dimensionless particle diameter and the Reynolds number, meaning that the estimation of the settling velocity is quick and easy. This formula is compared with expressions available elsewhere and its improved accuracy is demonstrated. When the formula was applied to Hallermeier's database [(1981). Terminal settling velocity of commonly occurring sand grains. Sedimentology 28(6), 859-865], which has been used in previous studies to develop settling velocity equations, it was also found to have the smallest root mean square error. The equation reported in the paper is one of very few expressions specifically developed for calcareous sand.

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Section: Methodsmentioning

confidence: 99%

Simple settling velocity formula for calcareous sand

Alcerreca

Silva

Mendoza

2013

Journal of Hydraulic Research

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“…Chaotic paths of freely falling and ascending spheres, path instabilities, and transitions in Newtonian fluid have been discussed by many (Jenny et al, 2004;Veldhuis and Biesheuvel, 2007;Horowitz and Williamson, 2010;Zhou and Dušek, 2015;Auguste and Magnaudet, 2018;Riazi and Türker, 2019) and experimentally proven by Raaghav (2019). To investigate the path trajectories expected for our particles, we investigated the state diagram (Zhou and Dušek, 2015) of the Galileo number Ga versus the density ratio ρ p /ρ f in Fig.…”

Section: Path Trajectoriesmentioning

confidence: 99%

“…Irregularly shaped particles Clift (1978) Haider and Levenspiel (1989) Concha and Almendra (1979) Ganser (1993) Brown and Lawler (2003) * Loth ( 2008) Almedeij (2008) Hölzer and Sommerfeld ( 2008) Cheng (2009) Yang et al ( 2015) Barati et al (2014) Ouchene et al ( 2016) Song et al (2017) Bagheri and Bonadonna (2016) Auguste and Magnaudet (2018) Dioguardi et al (2018) Goossens ( 2019) Breakey et al (2018) tems are limited (Dabrowski et al, 2008;Hunce et al, 2018).…”

Section: Spherical Particlesmentioning

confidence: 99%

Can terminal settling velocity and drag of natural particles in water ever be predicted accurately?

Kramer

Moel²,

Raaghav

et al. 2021

Drink. Water Eng. Sci.

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Abstract. Natural particles are frequently applied in drinking water treatment processes in fixed bed reactors, fluidised bed reactors, and sedimentation processes to clarify water and to concentrate solids. When particles settle, it has been found that, in terms of hydraulics, natural particles behave differently when compared to perfectly round spheres. To estimate the terminal settling velocity of single solid particles in a liquid system, a comprehensive collection of equations is available. For perfectly round spheres, the settling velocity can be calculated quite accurately. However, for naturally polydisperse non-spherical particles, experimentally measured settling velocities of individual particles show considerable spread from the calculated average values. This work aims to analyse and explain the different causes of this spread. To this end, terminal settling experiments were conducted in a quiescent fluid with particles varying in density, size, and shape. For the settling experiments, opaque and transparent spherical polydisperse and monodisperse glass beads were selected. In this study, we also examined drinking-water-related particles, like calcite pellets and crushed calcite seeding material grains, which are both applied in drinking water softening. Polydisperse calcite pellets were sieved and separated to acquire more uniformly dispersed samples. In addition, a wide variety of grains with different densities, sizes, and shapes were investigated for their terminal settling velocity and behaviour. The derived drag coefficient was compared with well-known models such as the one of Brown and Lawler (2003). A sensitivity analysis showed that the spread is caused, to a lesser extent, by variations in fluid properties, measurement errors, and wall effects. Natural variations in specific particle density, path trajectory instabilities, and distinctive multi-particle settling behaviour caused a slightly larger degree of the spread. In contrast, a greater spread is caused by variations in particle size, shape, and orientation. In terms of robust process designs and adequate process optimisation for fluidisation and sedimentation of natural granules, it is therefore crucial to take into consideration the influence of the natural variations in the settling velocity when using predictive models of round spheres.

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“…Previous studies showed that measured suspension velocity of particles in bounded mediums is lower than those measured in unbounded mediums. [61][62][63][64][65][66][67] This reduction in high Reynolds numbers is a function of particle cross section area to cross section area of the suspension column, λ = A P /A c . Awbi and Tan 64 measured drag coefficients of spheres in the range of λ greater than 0.06 in a square cross section wind tunnel and Reynolds number between 10 4 and 2 × 10 5 .…”

Section: Estimation Of Errorsmentioning

confidence: 99%

Dedicated vertical wind tunnel for the study of sedimentation of non-spherical particles

Bagheri

Bonadonna

Manzella

et al. 2013

Review of Scientific Instruments

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A dedicated 4-m-high vertical wind tunnel has been designed and constructed at the University of Geneva in collaboration with the Groupe de compétence en mécanique des fluides et procédés énergétiques. With its diverging test section, the tunnel is designed to study the aero-dynamical behavior of non-spherical particles with terminal velocities between 5 and 27 ms(-1). A particle tracking velocimetry (PTV) code is developed to calculate drag coefficient of particles in standard conditions based on the real projected area of the particles. Results of our wind tunnel and PTV code are validated by comparing drag coefficient of smooth spherical particles and cylindrical particles to existing literature. Experiments are repeatable with average relative standard deviation of 1.7%. Our preliminary experiments on the effect of particle to fluid density ratio on drag coefficient of cylindrical particles show that the drag coefficient of freely suspended particles in air is lower than those measured in water or in horizontal wind tunnels. It is found that increasing aspect ratio of cylindrical particles reduces their secondary motions and they tend to be suspended with their maximum area normal to the airflow. The use of the vertical wind tunnel in combination with the PTV code provides a reliable and precise instrument for measuring drag coefficient of freely moving particles of various shapes. Our ultimate goal is the study of sedimentation and aggregation of volcanic particles (density between 500 and 2700 kgm(-3)) but the wind tunnel can be used in a wide range of applications.

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Wall effects on the velocities of a single sphere settling in a stagnant and counter-current fluid and rising in a co-current fluid

Cited by 32 publications

References 35 publications

Simple settling velocity formula for calcareous sand

Simple settling velocity formula for calcareous sand

Can terminal settling velocity and drag of natural particles in water ever be predicted accurately?

Dedicated vertical wind tunnel for the study of sedimentation of non-spherical particles

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