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Experiment and numerical simulation of Taylor–Couette flow controlled by oscillations of inner cylinder cross section

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Abstract

An experimental and numerical study of the controlled Taylor–Couette flow with free surface is presented in this work. It is aimed to carry out a controlling strategy based upon a combination of free surface effect and an inner cylinder cross section oscillation. Numerical simulations are performed using FLUENT software package for three-dimensional incompressible flows. The basic system geometry is characterized by a height H = 170 mm, an inner and outer cylinders with, respectively, R1 = 31.5 mm and R2 = 35 mm, a ratio of the inner to outer cylinder radii ɳ = 0.9, an aspect ratio Γ = 28.5 and a ratio of the gap to the inner cylinder radius, δ = 0.1. It is established that the first and the second instabilities are delayed. The Taylor vortices and Ekman cells can be destroyed throughout a process applicable for all the flow regimes encountered in the Taylor–Couette flow. The Taylor vortices show a particular sensitivity and can be easily destroyed using low deforming frequencies (f < 3 Hz). The Ekman cells, however, exhibit larger resistance to actuation and substantially higher deforming frequencies (f > 20 Hz) are required for the complete disappearance.

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Abbreviations

u r , u θ , u z :

Velocity components

r,θ,z :

Cylindrical coordinates

Ta = \(Re\sqrt \delta\) :

Taylor number

Ta c :

Critical Taylor number

\(\upsilon\) :

Kinematic viscosity

f :

Frequency

R 1, R 2 :

Inner and outer cylinder radii

ρ :

Density

Ω 1, Ω 2 :

Inner and outer cylinder angular velocities

H f :

Height of working fluid

H :

Height of cylinders

\(\dot{m}_{\text{pq}} ,\;\dot{m}_{\text{qp}}\) :

Mass transfer between phases

R max :

Maximum limit of the oscillating inner cylinder

R(t) :

Instantaneous radius of the oscillating inner cylinder

d = R 2 − R 1 :

Annular gap

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

Oscillating amplitude

λ :

Axial wave number

Λ :

Axial wavelength

Γ = \(\frac{{H_{f} }}{d}\) :

Aspect ratio

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

Ratio of the radii

\(\delta\) = \(\frac{{R_{1} }}{d}\) :

Gap ratio

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

Reynolds number

α :

Volume fraction

C :

Cell Volume

p, q :

Phases (air and liquid)

T :

Cycle of deformation

d max, d min :

Annular gap limits

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Authors and Affiliations

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

    A. Abdelali, H. Oualli, A. Rahmani & B. Merzkane

  2. Laboratory of Thermodynamic and Energetical Systems, USTHB, Bab Ezzouar, 16032, Algiers, Algeria

    A. Bouabdallah

Authors
  1. A. Abdelali
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  2. H. Oualli
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  3. A. Rahmani
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  4. B. Merzkane
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  5. A. Bouabdallah
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Correspondence to A. Abdelali.

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Abdelali, A., Oualli, H., Rahmani, A. et al. Experiment and numerical simulation of Taylor–Couette flow controlled by oscillations of inner cylinder cross section. J Braz. Soc. Mech. Sci. Eng. 41, 259 (2019). https://doi.org/10.1007/s40430-019-1758-z

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  • DOI: https://doi.org/10.1007/s40430-019-1758-z

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