Mechanism of Vortices Appearance in the Taylor-Couette Flow System

Document Type : Regular Article


1 Laboratory of Fluid Mechanics, Military Polytechnical school, Bordj El Bahri, 16046 Alger. Algeria

2 Laboratory of Thermodynamics and Energetic Systems, USTHB, Bp 32 El-Alia, Alger, 16111, Algeria


This work is devoted to study the Taylor-Couette flow at the early structuring stages. It is aimed to gain insight on the Taylor and Ekman vortices genesis mechanism since the first hints of presence detected at Ta=10-4. Simulations are carried out using Ansys Fluent software package. The basic system geometry is characterized bya height H= 150mm, ratio of inner to outer cylinder radii η= 0.9, radial gap δ= 0.11 and an aspect ratio corresponding to system height reported togap length, Г= H/δ = 15. Ekman and Taylor cells are tackled since the Taylor number Ta=10-4 to the first (TVF) and second (WVF) instabilities settlement at Tac1= 43.8 and Tac2= 54, respectively. It is sought to shed light on the underlying mechanism responsible for flow genesis and to identify all the intermediate successive steps from ex-nihilo when the system is at rest up to complete vortices formation. The obtained results show that presence of Ekman cells is already perceptible since a Taylor number as low as Ta= 10-4. In fact, localized overpressure zones are detected on system inner endcaps surfaces regularly distributed according to a π/2 phase lag. These overpressure zones azimuthally propagate to meet and cover the entire gap circumference when Ta~10-2 to10-1.


Abcha, N., N. Latrache, F. Dumouchel and I. Mutabazi (2008). Qualitative relation between reflected light intensity by Kalliroscope flakes and velocity field in the Couette- Taylor flow system.Experiments in Fluids (45), 85–94.##
Abdelali, A., H. Oualli and A. Bouabdallah (2019). Experiment and numerical simulation of Taylor–Couettefow controlled by oscillations of inner cylinder cross section. Journal of the Brazilian Society of Mechanical Sciences and Engineering 41, 259.##
Adnane, E. and A. Bouabdallah (2016). Experimental Study of the Laminar-Turbulent Transition in a Tilted Taylor-Couette System Subject to Free Surface Effect. Journal of Applied Fluid Mechanics 9(3), 1097-1104.##
Ahlers, G. and D. S. Cannell (1983). Vortex-front propagation in rotating Couette-Taylor flow. Physical Review Letters 50, 1583–1586.##
Andereck, C. D., S. S. Liu and H. L. Swinney (1986). Flow regimes in a circular Couette system with independently rotating cylinders. Journal of Fluid Mechanics 164, 155-183.##
Bouabdallah, A. (1980). Instabilités et turbulence dans l’écoulement de Taylor–Couette, PhD Thesis, INPL, France.##
Coles, D. (1965). Transition in circular Couette flow. Journal of Fluid Mechanics 21, 385–425.##
Couette, M. M. (1890). Etudes sur le frottement des liquides. Annex of Chemistry Physics 433.##
Czarny, O., E. Serre, P. Bontoux and R. M.  Lueptow (2002). Spiral and wavy vortex flows in short counter-rotating Taylor–Couette cells. Theoret. Comput. Fluid Dynamics 16, 5–15.##
Czarny, O., E. Serre, P. Bontoux and R. M. Lueptow (2003). Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow. Physics of Fluids 15, 467–477.##
Czarny, O., E. Serre, P. Bontoux and R. M. Lueptow (2004). Ekman vortices and the centrifugal instability in counter-rotating cylindrical Couette flow. Theoretical and Computational Fluid Dynamics 18, 151–16.##
Denis, M., S. Eric and R. M. Lueptow(2014). Mechanisms for the transition to waviness for Taylor vortices. Physics of Fluids 26, 094102##
Fenstermacher, P. R. and H. L. Swinney (1979). Dynamical instabilities and the transition to chaotic Taylor vortex flow. Journal of Fluid Mechanics 94, part 1, 103-128.##
Goharzadeh, A. and I. Mutabazi (2001). Experimental characterization of intermittency regimes in the Couette–Taylor system. European Physical Journal B 19, 157–162.##
Gollub, J. P. and H. L. Swinney (1975). Onset of turbulence in a rotating fluid. Physical Review Letters 35, 927-930.##
Koschmeider, E. L. (1993). Bénard cells and Taylor vortices. Journal of Fluid Mechanics 253, 722-723.##
Lücke, M., M. Mihelcic and K. Wingerath (1985). Front propagation and pattern formation of Taylor vortices growing into unstable circular Couette flow. Physical Review A 31, 396–409.##
Ludwieg, H. (1964). Experimentelle Nachprüfung des Stabilitäts theorien für reibungsfreie StrömungenMitschraubenlinienförmigen Stromlinien. Z. Flugwiss 12, 304–309.##
Margules, M. (1881). Uber die bestimmung des reibungs-und gleitungs-coefficient, Wiener Berichte (second series) 83, 588-602.##
Oualli, H., S. Hanchi and A. Bouabdallah (2013). Taylor-Couette flow control using the outer cylinder cross-section variation strategy. European Physical Journal Applied Physics 61, 11102.##
Pfister, G. and I. Rehberg (1981). Space-dependent order parameter in circular Couette flow transitions. Physical Letters 83A, 19–22.##
Rayleigh, L. (1916). On the dynamics of revolving fluids. proceedings of the royal society of London, A, 148-154.##
Serre, E., M. A. Sprague and R. M. Lueptow (2008).Stability of Taylor–Couette flow in a finite-length cavity with radial throughflow. Physics of Fluids 20, 034106.##
Stockes, G. G. (1880). Mathematical and physical papers. Cambridge. U. P, England.##
Taylor, G. I. (1923). Stability of a viscous liquid contained between two rotating cylinders. Philosophical Transactions of the Royal Society A. London, 223, 289-343.##