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An experimental study of hydrodynamic behavior of rotating spherical particles in a quiescent viscous fluid

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Abstract

The motion of solids in a viscous fluid with nonlinear complex behavior has important applications in different industries and engineering sciences. This work experimentally investigated the free-fall behavior of rotating and non-rotating spherical particles in a viscous fluid. The effects of physical parameters, including particle size, particle density, fluid viscosity, and rotational velocity, on the terminal velocity of the falling spherical particles were examined. A high-speed camera was employed to capture the phenomena and study the free-fall behavior of the spherical solid particles in a viscous fluid. The studied spherical particles had five different densities of 2800, 7800, 7900, 8660, and 8960 kg/m3 and three varying dimensions of 4, 5, and 6 mm. To explore the effect of fluid viscosity on the terminal velocity of particles, two types of fluids with the viscosities of 0.012 and 0.014 Pa.s were used. The initial rotational velocities were 0, 600, 900, and 1200 rpm for the falling particles. The obtained results revealed that increases in the particle diameter, density, and rotational velocity, along with a decrease in fluid viscosity, accelerated the terminal velocity and shortened the time of reaching this velocity. Furthermore, an increase in the Reynolds number gave rise to a decrease in the lift coefficient. On the other hand, the accelerated dimensionless rotational velocity increased the lift coefficient.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

Abbreviations

\(m_{p}\) :

Particle mass (kg)

\(\mu_{f}\) :

Fluid viscosity (Pa.s)

\(u_{f}\) :

Fluid velocity (Pa.s)

g :

Gravity (m/s2)

\(u_{p}\) :

Rticle velocity (cm/sec)

\(F_{B}\) :

Basset force (N)

\(F_{M}\) :

Weight force (N)

\(F_{D}\) :

Drag force (N)

\(F_{b}\) :

Bouncy force (N)

\(F_{L}\) :

Lift force (N)

\(\rho_{f}\) :

Fluid density (kg/m3)

\(\rho_{s}\) :

Particle density (kg/m3)

\(C_{L}\) :

Lift coefficient

\(C_{D}\) :

Drag coefficient

\({\text{Re}}_{p}\) :

Reynolds number

\(d_{{{\text{sph}}}}\) :

Spherical diameter (mm)

\(d_{*}\) :

Dimensionless diameter

\(U_{*}\) :

Dimensionless speed

\(w\) :

Rotational velocity (rpm)

\(A\) :

Area (mm2)

\(C_{a}\) :

Added mass coefficient

\(F_{m}\) :

Added mass force (N)

\(d_{p}\) :

Particle diameter (mm)

t :

Time (sec)

\(u_{r}\) :

Relative velocity (cm/sec)

MA1:

Acceleration parameter

\(\tau\) :

Time constant

\(\gamma\) :

Dimensionless angular velocity

S :

Solid material

F :

Fluid

P :

Particle

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Authors and Affiliations

  1. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    H. Dehgan, M. H. Nobakhti & M. Khayat

  2. Department of Mechanical Engineering, Tabriz Branch, Islamic Azad University, Tabriz, Iran

    E. Esmaeilzadeh & A. Rostamzadeh Khosroshahi

Authors
  1. H. Dehgan
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  2. M. H. Nobakhti
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  3. E. Esmaeilzadeh
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  4. M. Khayat
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  5. A. Rostamzadeh Khosroshahi
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Correspondence to M. H. Nobakhti.

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Dehgan, H., Nobakhti, M.H., Esmaeilzadeh, E. et al. An experimental study of hydrodynamic behavior of rotating spherical particles in a quiescent viscous fluid. Eur. Phys. J. Plus 136, 967 (2021). https://doi.org/10.1140/epjp/s13360-021-01795-0

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