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

  • A. AbdelaliEmail author
  • H. Oualli
  • A. Rahmani
  • B. Merzkane
  • A. Bouabdallah
Technical Paper


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.


Taylor–Couette flow Flow control Inner cylinder oscillation Taylor vortices Ekman cells 

List of symbols

ur, uθ, uz

Velocity components


Cylindrical coordinates

Ta = \(Re\sqrt \delta\)

Taylor number


Critical Taylor number


Kinematic viscosity




Inner and outer cylinder radii



Ω1, Ω2

Inner and outer cylinder angular velocities


Height of working fluid


Height of cylinders

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

Mass transfer between phases


Maximum limit of the oscillating inner cylinder


Instantaneous radius of the oscillating inner cylinder

d = R2 − R1

Annular gap

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

Oscillating amplitude


Axial wave number


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


Volume fraction


Cell Volume

p, q

Phases (air and liquid)


Cycle of deformation

dmax, dmin

Annular gap limits


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Laboratory of Fluid MechanicsEcole Militaire Polytechnique (EMP)AlgiersAlgeria
  2. 2.Laboratory of Thermodynamic and Energetical SystemsUSTHBAlgiersAlgeria

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