Axial Flow Effect on the Stability of Circular Couette Flow

Document Type : Regular Article


1 Laboratory of Modelisation and SImulation in Fluid Mechanics (LAMOSI), University of Sciences and Technology of Oran, USTO-MB, 31000, Oran, Algeria

2 LaSIE, UMR 7356, University of La Rochelle, La Rochelle, France

3 Laboratory of Fluid Mechanics, Ecole Militaire Polytechnique (EMP), Borj El Bahri, 16111 Algiers, Algeria

4 Laboratory of Thermodynamic and Energetical Systems (LTSE), USTHB, Bab Ezzouar, 16032 Algiers, Algeria


We investigate the effect of an axial Poiseuille annular flow on the stability of Taylor vortices via numerical simulation using CFD Ansys Fluent software. The working conditions are identical to those of the Taylor-Couette experimental device of the LaSIE laboratory, where the inner cylinder is rotated. An incompressible fluid of density ρ= 998 kg/m3, with a kinematic viscosity m2/s at a temperature T= 19.5 °C is considered. The geometrical parameters of the flow system are characterized by a height H=275 mm, a radius ratio η=0.804, and an axial aspect factor Γ=45.45. The axial Reynolds number and Taylor number are respectively in the ranges of  , and . Flow control is carried out according to two distinct protocols to bring out the effect of axial flow on the evolution of the Taylor vortex Flow (TVF). The first consists of superimposing an azimuthal flow around the critical TVF threshold with increasing axial flow until the Taylor vortices disappear. In the second, an axial field is set and the Taylor number is varied until onset of the TVF mode. It is predicted that in the presence of an axial flow, the critical threshold for first instability triggering (TVF) is delayed. In addition, the ratio of the axial phase velocity to the mean axial velocity of the axial base flow is 1.16. This value agrees well with previous results reported in literature.


Abdelali, A., H. Oualli, A. Rahmani, B. Merzkane and A. Bouabdallah (2019). Experiment and numerical simulation of Taylor – Couette flow controlled by oscillations of inner cylinder cross-section. Journal of the Brazilian Society of Mechanical Sciences and Engineering 41(6), 1–8.##
Ali, M. E., D. Mitra, J. A. Schwille and R. M. Lueptow (2002). Hydrodynamic stability of a suspension in cylindrical Couette flow. Physics of Fluids 14 (3).##
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. Ph. D. thesis, INPL, Nancy, France.##
Burkhalter, J. E. and E. L. Koschmieder (1973). Steady supercritical Taylor vortex flow. Journal of Fluid Mechanics 58 part 3, 547-560.##
Chandrasekhar (1961). Hydrodynamic and hydromagnetic stability. Dover Publications.##
Coles (1965). Transition in circular Couette flow. Journal of Fluid Mechanics 21,385-425.##
DiPrima, R. C. and A. Pridor (1979). The stability of viscous flow between rotating concentric cylinders with an axial flow. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 366, 555.##
Drazin, F. and W. H. Reid (1981). Hydrodynamic stability. Cambridge University Press.##
Fenstermacher, P. R., H. L. Swinney and J. P. Gollub (1979). Dynamical instabilities and transition to chaotic Taylor vortex flow. Journal of Fluid Mechanics 94, part1,103-128.##
Hwang, J. Y. and K. S. Yang (2004). Numerical study of Taylor–Couette flow with an axial flow. Computers and Fluids 33, 97–118.##
Kataoka, K., H. Doi and T. Komai (1977). Heat and mass transfer in Taylor vortex flow with constant axial flow rates. International Journal of Heat and Mass Transfer 20, 57–63.##
Kristiawan, M., M. El Hassan, A. El Faye and V. Sobolík (2019). Experimental investigation of Taylor-Couette-Poiseuille flow at low Taylor and Reynolds numbers. PLoS ONE 14(4), 1–21.##
Lueptow, R. M., A. Docter and K. Min (1992). Stability of axial flow in an annulus with a rotating inner cylinder. Physics of Fluids A 4(11), 2446–2455.##
Lueptow R. M. and S. T. Wereley (1999). Velocity field for Taylor–Couette flow with an axial flow. Physics of Fluids 11(12), 3637–3649.##
Monfared, M. and E. Shirani (2016). Numerical and experimental study on the flow history effects of axial flow on the Couette–Taylor flow. Springer-Verlag Wien 227(7), 1999-2010.##
Ng, B. S. and E. R. Turner (1982). On the linear stability of spiral flow between rotating cylinders. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 382, 83–102.##
Ohmura, N., T. Suemasu and Y. Asamura (2005).  Particle classification in Taylor vortex flow with an axial flow. Journal of physics: Conference Series (14), 64-71.##
Recktenwald, A., M. Lucke, and H. W. Muller (1993). Taylor vortex formation in axial through-flow. Linear and weakly nonlinear analysis, Physical Review E 48(6), 4444.##
Tsameret, A. and V. Steinberg (1994). Absolute and convective instabilities and noise-sustained structures in the Couette–Taylor system with an axial flow. Physical Review E, 49, 1291– 1308.##
Wereley, S. T. and R. M. Lueptow (1998). Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. Journal of Fluid Mechanics364, 59–80.##
Volume 15, Issue 1 - Serial Number 63
January and February 2022
Pages 271-281
  • Received: 17 June 2021
  • Revised: 05 September 2021
  • Accepted: 11 September 2021
  • First Publish Date: 19 November 2021