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Bubbles injection effect on Taylor–Couette flow controlled by deformations of inner cylinder cross-section

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Abstract

A numerical simulation is carried out to make investigation of bubbles interactions when injected in Taylor–Couette system. This process can affect the flow patterns, especially when it is combined with inner cylinder cross-section oscillations. The included phase is modeled by the Lagrangian approach. The flow regime range is considered until the onset of the wavy Taylor vortex flow (low regime). We attempt to characterize bubbles dispersion effects on the drag force near the inner-cylinder while it is executing radial sinusoidal deformations. It is assumed that the obtained configurations of air-bubbles accumulations are compared for validation with experimental and numerical studies from the literature. The bubbles have uniform spherical shape with a diameter Db = 0.06d, where d is the system gap width. The inner cylinder oscillation is imposed using a sinusoidal law with a fixed deforming frequency and different amplitude ratios of the initial radius R1. Overall, without reaching a fully developed regime, the obtained results for a low Taylor number showed that the drag reduction ratio could be decreased when the inner cylinder is deformed.

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Abbreviations

R 2, R 1 :

Outer and inner cylinder radius

Ω 1, Ω 2 :

Inner and outer cylinder angular velocities

H f :

Height of working fluid

Hc:

Height of cylinders

R max :

Limit of the oscillating cylinder

R(t):

Instantaneous radius

Tac :

Critical Taylor number

Ta = Re\(\sqrt {\delta}\) :

Taylor number

d = R 2 –R 1 :

Annular gap

\(\overline{\overline{\tau }}\) :

Stress tensor

r, θ, z :

Cylindrical coordinates

Re = \(\frac{{\Omega_{1} .R_{1} .d}}{\upsilon }\) :

Reynolds number

T :

Cycle of deformation

d i, d f :

Initial and final annular variable gap

f :

Frequency

U TV :

Axial Taylor vortices velocity

\(e_{{\text{n}}} , e_{{\text{t}}}\) :

Normal and tangential restitution coefficients

ρ :

Density

Γ = \(\frac{{H_{{\text{f}}} }}{d}\) :

Aspect ratio

\(\eta\) = \(\frac{{R_{1} }}{{R_{2} }}\) :

Ratio of the radii

\(\delta\) = \(\frac{{R_{1} }}{d}\) :

Gap ratio

α :

Volume fraction

ε = \(\frac{{R_{{{\text{max}}}} - R_{1} }}{{R_{1} }}\) :

Oscillating amplitude

C ws :

Wall shear stress

Cv:

Cell volume

H, C :

Dimensionless parameters

R b :

Bubble radius

U f :

Fluid velocity

R b, D b :

Bubble radius and diameter

\(\nu_{{\text{b}}}\) :

Bubble volume

V b :

Bubble velocity rise

Q b :

Flow rate injection

C D, C L :

Drag and lift coefficients of bubbles

\(\vec{F}\) :

External body forces

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Authors and Affiliations

  1. Laboratory of Fluid Mechanics, Ecole Militaire Polytechnique (EMP), 16111, Bordj El Bahri, Algiers, Algeria

    A. Abdelali, H. Oualli & S. Hanchi

  2. Laboratoy of Tharmodynamic and Energetic Systems, USTHB, 16032, Bab Ezzouar, Algiers, Algeria

    A. Bouabdallah

Authors
  1. A. Abdelali
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  2. H. Oualli
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  3. S. Hanchi
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  4. A. Bouabdallah
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Correspondence to A. Abdelali.

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Technical Editor: Erick Franklin.

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Abdelali, A., Oualli, H., Hanchi, S. et al. Bubbles injection effect on Taylor–Couette flow controlled by deformations of inner cylinder cross-section. J Braz. Soc. Mech. Sci. Eng. 43, 214 (2021). https://doi.org/10.1007/s40430-021-02930-9

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  • DOI: https://doi.org/10.1007/s40430-021-02930-9

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