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Investigation of the effect of small bubbles on energy dissipation in a vertical Couette–Taylor system

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Abstract

The effect of small bubbles on reduction of energy dissipation has been numerically investigated in a vertical Couette–Taylor system. Flow is in the annular space between two concentric cylinders as the internal cylinder is rotating while the outer cylinder is stationary. Main fluid between cylinders is silicone, while air bubbles are constantly injected into the main flow at the bottom of cylinders’ gap. The air bubbles rise through the flow when they are injected into the silicone flow. The flow is fully turbulence and Taylor vortices have appeared in the annulus gap. The rotational Reynolds number (Reω) varies from 700 to 3000. The fully two-phase turbulent flow has been studied using a discrete phase model and Euler–Lagrange approach. Air bubbles distribution or bubbles pattern through the main flow, which is acquired using numerical method, shows a good agreement to those acquired via experimental data in all Reynolds numbers. To investigate the changes of skin friction drag, the rate of energy dissipation in the system is calculated. The effect of injected air with constant flow rate on the total energy dissipation rate and the drag coefficient is also investigated. The results confirmed reduction of energy dissipation and about 25% of drag reduction when small bubbles were injected in the system. This reduction was the effect of the bubbles on the density of fluid and transformed momentum. Moreover, the acquired numerical results were in good agreement with those found in the previous experimental works, in which maximum Reω is up to 3000.

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Abbreviations

F D :

Drag force

Fr:

Froude number

G :

Gravity (m/s2)

I :

Turbulence intensity

M :

Mach number

Q :

Volume rate (m3/s)

Re :

Reynolds number

R :

Radius

Ta:

Taylor number

U :

The average velocity

U :

Velocity(m/s)

u′:

Velocity in Reynolds stress (m/s)

νw :

The kinematic viscosity of the pure water

Y :

Dissipation term

We:

Weber number

B :

Bubble

D :

Drag

K :

Power gain factor

i :

X direction

j :

Y direction

k :

Z direction

T :

Temperature

α :

Volume fraction (closure coefficient in the dissipation rate equation)

β*:

Closure coefficient in the turbulent-kenetic energy equation

δ :

Radial gap

σ :

Surface tension

μ :

Viscosity

μ t :

Turbulence viscosity

ω :

Energy dissipation rate

ρ :

Density (kg/m3)

Ω :

Vorticity

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Authors and Affiliations

  1. Department of Mechanical Engineering, Bozorgmehr University of Qaenat, Qaen, Iran

    Mohammad Hossein Shafiei Mayam

  2. Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

    Reza Maryami

  3. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Mohammad Mustafa Ghafurian

Authors
  1. Mohammad Hossein Shafiei Mayam
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  2. Reza Maryami
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  3. Mohammad Mustafa Ghafurian
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Correspondence to Mohammad Hossein Shafiei Mayam.

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Technical Editor: Jader Barbosa Jr.

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Shafiei Mayam, M.H., Maryami, R. & Ghafurian, M.M. Investigation of the effect of small bubbles on energy dissipation in a vertical Couette–Taylor system. J Braz. Soc. Mech. Sci. Eng. 40, 244 (2018). https://doi.org/10.1007/s40430-018-1063-2

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  • DOI: https://doi.org/10.1007/s40430-018-1063-2

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