Annular flow dynamic characteristics of two inverse coaxial rotational cones

  • He Zou
  • Shang Li
  • Feng Bao
  • Zhirong LiuEmail author
  • Rui ZhuEmail author
Regular Paper


Dye liquid visualization and PIV experiments were conducted to reveal the influence of the Reynolds number (Re) and the presence of an end plate at the upper boundary on the annular flow dynamics characteristics of coaxial cones. The key flow information, such as the vorticity and velocity distributions, time-averaged flow field, and Reynolds stresses, were obtained by processing the velocity field. The Taylor vortex dynamics mechanism was studied based on the quantitative evaluation of the periodic vortex transformations. The experimental results showed that there was upward flow in the annulus at very low Reynolds numbers (Re = 107 and 160), and the annular flow transitioned from an upward to a downward pattern as Re (Re ≥ 214) increased. The first vortex was always separated by a negative vortex, B2, generated in the top right corner for Re = 214–642. A counterclockwise vortex under the free water surface always formed because the centrifugal force dominated at the water level, and there was always a fixed clockwise vortex under the upper cap because the dynamic pressure dominated at the non-slip wall surface for Re = 214–1925. The dominant convex outward or concave inward flow reflected the dominant motive source force. The total Reynolds stress increased with the increase in Re, and the magnitudes of the stresses were in the following order: radial normal stress > axial normal stress > shear stress.

Graphic abstract


Annulus Cone PIV Vortex Reynolds stress 



The funding for this study was received from Joint Pre-research Foundation of Military Equipment Department and Ministry of Education (6141A02033529); National Natural Science Foundation of China (11072206); and Natural Science Foundation of the Fujian Province, China (2012J01023).


  1. Aujogue K, Pothérat A et al (2018) Experimental study of the convection in a rotating tangent cylinder. J Fluid Mech 843:355–381CrossRefGoogle Scholar
  2. Bao F, Zeng HL, Zou H et al (2018) Mechanism and experimental research on fluid flow in annulus of coaxial rotating conical cylinders. J Beijing Univ Aeronaut Astronaut 44(8):1577–1586Google Scholar
  3. Canuto D, Taira K (2015) Two dimensional compressible viscous flow around a circular cylinder. J Fluid Mech 785:349–371MathSciNetCrossRefzbMATHGoogle Scholar
  4. Daniel BE (2014) Subcritical transition to turbulence in Taylor–Couette flow. Georgia Institute of TechnologyGoogle Scholar
  5. Elbaz S, Gat A (2016) Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube. J Fluid Mech 806:580–602MathSciNetCrossRefzbMATHGoogle Scholar
  6. Fardin MA, Perge C, Taberlet N (2014) “The hydrogen atom of fluid dynamics”—introduction to the Taylor–Couette flow for soft matter scientists. Soft Matter 10(20):3523–3535CrossRefGoogle Scholar
  7. Flór JB, Hirschberg L, Oostenrijk BH et al (2018) Onset of centrifugal instability at a rotating cylinder in a stratified fluid. Phys Fluids 30(8):084103CrossRefGoogle Scholar
  8. Grossmann S, Lohse D, Sun C (2016) High-Reynolds number Taylor–Couette turbulence. Annu Rev Fluid Mech 48(48):53–80MathSciNetCrossRefzbMATHGoogle Scholar
  9. Li X, Zhang J et al (2014) A numerical investigation of flow between rotating conical cylinders of two different configurations. J Hydrodyn 26(3):431–435CrossRefGoogle Scholar
  10. Majji MV, Morris JF (2018) Inertial migration of particles in Taylor–Couette flows. Phys Fluids 30(3):033303CrossRefGoogle Scholar
  11. Munir A, Zhao M, Wu H et al (2018) Three-dimensional numerical investigation of vortex-induced vibration of a rotating circular cylinder in uniform flow. Phys Fluids 30(5):053602CrossRefGoogle Scholar
  12. Narasimhamurthy VD, Andersson HI, Pettersen B (2014) Novel features of a fully developed mixing-layer between co-flowing laminar and turbulent Couette flows. Phys Fluids 26(3):031703CrossRefGoogle Scholar
  13. Noui-Mehidi MN, Wimmer M (1999) Free surface effects on the flow between conical cylinders. Acta Mesh 135:13–25zbMATHGoogle Scholar
  14. Noui-Mehidi MN, Ohmura N, Kataoka K (2005) Dynamics of the helical flow between rotating conical cylinders. J Fluids Struct 20(3):331–344CrossRefGoogle Scholar
  15. Ohmura N, Kataoka K, Mizumoto T et al (2005) Effect of vortex cell structure on bifurcation properties in a Taylor vortex flow system. J Chem Eng Jpn 28(6):758–764CrossRefGoogle Scholar
  16. Ostilla-Mónico R, Verzicco R et al (2016) Turbulent Taylor-Couette flow with stationary inner cylinder. J Fluid Mech. MathSciNetzbMATHGoogle Scholar
  17. Ostilla-Mónico R, van der Poel EP, Verzicco R et al (2014) Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor–Couette flow. Phys Fluids 26(1):015114CrossRefGoogle Scholar
  18. Riahi M, Aniss S, Ouazzani Touhami M (2019) Families of reversing and non-reversing Taylor vortex flows between two co-oscillating cylinders with different amplitudes. Phys Fluids 31(1):014101CrossRefGoogle Scholar
  19. Sciacchitano A, Scarano F, Wieneke B (2012) Multi-frame pyramid correlation for time-resolved PIV. Exp Fluids 53(4):1087–1105CrossRefGoogle Scholar
  20. Seyed-Aghazadeh B, Modarres-Sadeghi Y (2015) An experimental investigation of vortex-induced vibration of a rotating circular cylinder in the crossflow direction. Phys Fluids 27(6):067101CrossRefGoogle Scholar
  21. Wimmer M (2000) Taylor vortices at different geometries. Phys Rotat Fluids 549:194–212CrossRefGoogle Scholar
  22. Wong K, Zhao J et al (2017) Experimental investigation of flow-induced vibration of a rotating circular cylinder. J Fluid Mech 829:486–511CrossRefGoogle Scholar
  23. Zhu H, Wang C et al (2017) Tomographic PIV investigation on 3D wake structures for flow over a wall-mounted short cylinder. J Fluid Mech 831:743–778CrossRefGoogle Scholar

Copyright information

© The Visualization Society of Japan 2019

Authors and Affiliations

  1. 1.School of Aerospace EngineeringXiamen UniversityXiamenChina

Personalised recommendations