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Particle flow fall process: a systematic study of entrained air under unconfined and semi-confined fall conditions

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Abstract

Industrial bulk material transfer and handling processes often result in large dust emissions and seriously threaten workers’ health. Both dust dispersion and ventilation for dust removal are related to the entrained air flow rate under the particle flow fall process. Based on the air jet theory, this paper presents a model for unconfined and semi-confined particle flow fall processes. Theoretical formulas for the entrained air flow rate were developed, and a numerical simulation was performed to analyze the particle velocity and entrained air under unconfined and semi-confined particle flow fall processes. The results show that as the distance from the particle source to the wall’s surface decreases, the particle velocity slightly increases; however, the value of the particle velocity always varies between that of unconfined fall and fall in vacuum. It is found that when the distance of the particle source from the wall’s surface s is less than five times the width of the particle source d (s < 5d), the entrained air flow can adhere well to the wall’s surface; and when s = 0d, the entrained air flow rate caused by the semi-confined particle flow fall process is minimal and is reduced by 22% compared to that of the unconfined fall.

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Abbreviations

A 0 :

Area of particle source (m2)

A ps :

Cross-sectional area of particle flow (m2)

A p :

Projected area of particle (m2)

b :

Width of the spout (m)

C D :

Drag coefficient dimensionless

d p :

Particle diameter (m)

d :

Width of the particle source (m)

f d :

Drag force on a single particle in quiescent air (N)

h :

Drop height (m)

\(\varepsilon_{core}\) :

Void fraction of the particle flow core zone dimensionless

m tot :

Mass flow rate of particle flow (kg s−1)

m a :

Mass flow rate of air within particle flow (kg s−1)

m p :

Mass flow rate of particles (kg s−1)

m s :

Mass of single particles (kg)

n :

Number of particles released from particle source in per second (s−1)

P t :

Total pressure of airflow (Pa)

P v :

Velocity pressure (Pa)

Q a :

Entrained air flow rate of unconfined particle flow fall (m3 s−1)

Q s :

Entrained air flow rate of semi-confined particle flow fall (m3 s−1)

Re:

Reynolds number dimensionless

s :

Distance of the particle source from the wall surface (m)

v a :

Airflow velocity (m s−1)

v p :

Particle velocity (m s−1)

v 0 :

Initial velocity of particle flow (m s−1)

v core :

The entrained air maximum velocity at different heights (m s−1)

V tot :

Volume occupied by particle flow (m3)

V p :

Volume occupied by particles in particle flow (m3)

V a :

Volume occupied by air in particle flow (m3)

W :

Work by particle flow (N m s−1)

x :

Distance to the spout (m)

y :

Different positions (m)

y core :

Particle flow core position (m)

μ a :

Air dynamic viscosity (N s m−2)

ρ p :

Particle density (kg m−3)

ρ core :

Density of particle flow core zone (kg m−3)

ρ a :

Air density (kg m−3)

η :

Distance from the position of va = vcore/2 to ycore (m)

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51678469).

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Authors and Affiliations

  1. School of Building Services Science and Engineering, Xi’an University of Architecture and Technology, Xi’an, 10055, Shaanxi, People’s Republic of China

    Hongfa Sun, Angui Li, Jifu Wu & Jing Zhang

  2. College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Hongfa Sun

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Correspondence to Angui Li.

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Sun, H., Li, A., Wu, J. et al. Particle flow fall process: a systematic study of entrained air under unconfined and semi-confined fall conditions. Granular Matter 22, 49 (2020). https://doi.org/10.1007/s10035-020-01018-w

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