Skip to main content
SpringerLink
Log in

Numerical and experimental study on the flow history effects of axial flow on the Couette–Taylor flow

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this research, experimental and numerical techniques are used to study the flow history effects of axial flow on the Couette–Taylor flow. For the experimental investigation, the flow is visualized using the PIV technique with reflective particles with a density of 1.62 g/cm3. Dispersed in a solution, the particles have a strong refraction index equal to 1.85. In this study, two protocols are adopted to study the effect of an axial flow superimposed on a Couette–Taylor flow, and of the history of the flow. The first one, the direct protocol, consists of imposing an azimuthal flow to the inner cylinder. In this case, when the regime is established, the axial flow is superimposed. The second protocol, the inverse protocol, consists of imposing first the axial flow in the gap of the system, after which an azimuthal flow is conveyed. The Couette–Taylor flow with axial flow is strongly dependent on the flow history (the protocol). Thus, the flow structures and development for different protocols are studied and analyzed here experimentally and numerically. In addition, from the numerical results, mathematical models for the two protocols are presented. For the direct protocol, a new relation between the axial Reynolds number, which stabilizes the Couette–Taylor flow, and the Taylor number is presented; for the inverse protocol, a new mathematical model for the critical Taylor number is developed as a function of the axial Reynolds number and also the first critical Taylor number without axial flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

d :

Length gap

R :

Radius

h :

Height

Ta :

Taylor number

Re :

Reynolds number

u :

Velocity

V :

Velocity

P :

Pressure

t :

Time

\({\eta}\) :

Radial ratio

\({\Gamma}\) :

Aspect ratio

\({\delta}\) :

The curvature

\({\Omega}\) :

Angular velocity

N :

Kinematic viscosity

\({\mu}\) :

Viscosity

\({\rho}\) :

Density

1:

Inner cylinder

2:

Outer cylinder

ax :

Axial flow

c:

Critical

*:

Dimensionless notation

References

  1. Cornish J.A.: Flow of water through fine clearances with relative motion of the boundaries. Proc. R. Soc. Lond. 140, 227–240 (1933)

    Article  Google Scholar 

  2. Goldstein S.: The stability of viscous fluid flow between rotating cylinders. Proc. Camb. Philos. Soc. 33, 41–61 (1937)

    Article  MATH  Google Scholar 

  3. Kaye J., Elgar E.C.: Modes of adiabatic and diabetic fluid flow in an annulus with an inner rotating cylinder. Trans. ASME 80, 753–765 (1958)

    Google Scholar 

  4. Donnelly R.J., Fultz D.: Experiments on the stability of spiral flow between rotating cylinders. Proc. Natl. Acad. Sci. USA 46, 1150 (1960)

    Article  MATH  Google Scholar 

  5. Chung K.C., Astill K.N.: Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow. J. Fluid Mech. 81, 641–655 (1977)

    Article  MATH  Google Scholar 

  6. Gravas N., Martin B.W.: Instability of viscous axial flow in annuli having a rotating inner cylinder. J. Fluid Mech. 86, 385–394 (1978)

    Article  Google Scholar 

  7. Meseguer A., Marques F.: On the competition between centrifugal and shear instability in spiral Poiseuille flow. J. Fluid Mech. 455, 129–148 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wereley S.T., Lueptow R.M.: Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. J. Fluid Mech. 364, 59–80 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wereley S.T., Lueptow R.M.: Velocity field for Taylor–Couette flow with an axial flow. Phys. Fluids 11(12), 3637–3649 (1999)

    Article  MATH  Google Scholar 

  10. Wouahbi, F.Z.: Étude de l’écoulement Taylor–Couette avec les sondes tri-segmentées électrochimiques. Thése de doctorat, Université de La Rochelle (2009)

  11. Berrich, E., Aloui, F., Legrand, J.: On the stability of Taylor–Couette flow with axial flow. In: ASME FEDSM, 7th Symposium on Flow Manipulation and Active Control, vol. 1, Parts A and B, FEDSM2012-72235, pp. 899–908, Rio Grande, Puerto Rico, USA, July 8–12 (2012)

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 8415683111, Iran

    Mostafa Monfared & Mohammad Reza Salimpour

  2. Department of Mechanical Engineering, Foolad Institute of Technology, Isfahan, 8491663763, Iran

    Ebrahim Shirani

  3. TEMPO, EA 4542, Universit’e Lille Nord de France, 59313, Valenciennes, France

    Fethi Aloui

Authors
  1. Mostafa Monfared
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ebrahim Shirani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Reza Salimpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fethi Aloui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Reza Salimpour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Monfared, M., Shirani, E., Salimpour, M.R. et al. Numerical and experimental study on the flow history effects of axial flow on the Couette–Taylor flow. Acta Mech 227, 1999–2010 (2016). https://doi.org/10.1007/s00707-016-1592-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-016-1592-7

Keywords

Search

Navigation