Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-14T03:10:05.616Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence generation and decay in the Taylor–Couette system due to an abrupt stoppage

Published online by Cambridge University Press:  07 May 2021

H. Singh Open the ORCID record for H. Singh [Opens in a new window]  and
A. Prigent Open the ORCID record for A. Prigent [Opens in a new window]
H. Singh
Affiliation:
Normandie Université, UniHavre, CNRS, UMR 6294, Laboratoire Ondes et Milieux Complexes (LOMC), 53, Rue Prony, CS 80 540 76058Le Havre, France
A. Prigent*
Affiliation:
Normandie Université, UniHavre, CNRS, UMR 6294, Laboratoire Ondes et Milieux Complexes (LOMC), 53, Rue Prony, CS 80 540 76058Le Havre, France
*
†Email address for correspondence: arnaud.prigent@univ-lehavre.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

This study presents an innovative approach towards the generation and decay of turbulence in the Taylor–Couette system. The outer cylinder was brought to an abrupt stoppage that generated turbulence in the system, which was initially in the laminar flow regime. Two complementary experimental approaches, namely visualizations and stereo-particle image velocimetry (PIV) measurements, were used to better understand the presented phenomenon for only external cylinder rotation. A moving time average technique was developed due to the continuous change in the length scales throughout the generation and decay process. The different stages of the generation and decay of turbulence were described and characterized through dynamic quantities such as the kinetic energy. This new approach towards the generation and decay of turbulence in the Taylor–Couette flow should help significantly in future endeavours.

JFM classification

Instability: Transition to turbulence Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A21
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Antonia, R.A., Djenidi, L., Danaila, L. & Tang, S.L. 2017 Small scale turbulence and the finite Reynolds number effect. Phys. Fluids 29, 020715.CrossRefGoogle Scholar
Batchelor, G.K., Townsend, A. & Taylor, G.I. 1948 a Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193, 539–598.Google Scholar
Batchelor, G.K., Townsend, A. & Taylor, G.I. 1948 b Decay of turbulence in the final period. Proc. R. Soc. Lond. A 194, 527–543.Google Scholar
Biferale, L., Boffeta, G., Celani, A., Lanotte, A., Toschi, F. & Vergassola, M. 2003 The decay of homogeneous anisotropic turbulence. Phys. Fluids 15, 2105–2112.CrossRefGoogle Scholar
Davidson, P.A. 2011 The minimum energy decay rate in quasi-isotropic grid turbulence. Phys. Fluids 23, 085108.CrossRefGoogle Scholar
Esser, A. & Grossmann, S. 1996 Analytic expression for Taylor–Couette stability boundary. Phys. Fluids 8, 1814.CrossRefGoogle Scholar
Euteneuer, A.G. & Karlsruhe, B.R.D. 1972 Die entwieklung von Längswirbeln in zeitlieh anwaehsenden grenzsehichten an konkaven wänden. Acta Mechanica 13, 215–223.CrossRefGoogle Scholar
Eyink, G.L. & Thomson, D.J. 2000 Free decay of turbulence and breakdown of self-similarity. Phys. Fluids 51, 477–479.CrossRefGoogle Scholar
George, W.K. 1992 The decay of homogeneous isotropic turbulence. Phys. Fluids A 4, 1492–1509.CrossRefGoogle Scholar
Huisman, S.G., van der Veen, R.C.A., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5, 3820.CrossRefGoogle ScholarPubMed
Hurst, D. & Vassilicos, J.C. 2007 Scalings and decay of fractal-generated turbulence. Phys. Fluids 19, 035103.CrossRefGoogle Scholar
Hussain, A.K.M.F. & Reynolds, W.C. 1970 The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech. 41, 241–258.CrossRefGoogle Scholar
Kaiser, F., Frohnapfel, B., Ostilla-Monico, R., Kriegseis, J., Rival, D.E. & Gatti, D. 2020 On the stages of vortex decay in an impulsively stopped, rotating cylinder. J. Fluid Mech. 885, A6.CrossRefGoogle Scholar
de Kármán, T. & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Phys. Lett. A 164, 192–215.Google Scholar
Kim, M.C. & Choi, C.K. 2004 The onset of Taylor–Görtler vortices in impulsively decelerating swirl flow. Korean J. Chem. Engng 21, 767–772.CrossRefGoogle Scholar
Kim, M.C. & Choi, C.K. 2006 The onset of Taylor–Görtler vortices during impulsive spin-down to rest. Chem. Engng Sci. 61, 6478–6485.CrossRefGoogle Scholar
Kim, M.C., Song, K.H. & Choi, C.K. 2008 Energy stability analysis for impulsively decelerating swirl flows. Phys. Fluids 20, 064101.CrossRefGoogle Scholar
Kohuth, K.R. & Neitzel, G.P. 1988 Experiments on the instability of an impulsively-initiated circular Couette flow. Exp. Fluids 6, 199–208.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 On degeneration (decay) of isotropic turbulence in incompressible viscous liquid. Dokl. Akad. Nauk SSSR 31, 538–540.Google Scholar
Lohse, D. 1994 Crossover from high to low Reynolds number turbulence. Phys. Rev. Lett. 24, 3223–3226.CrossRefGoogle Scholar
Mathis, D.M. & Neitzel, G.P. 1985 Experiments on impulsive spin-down to rest. Phys. Fluids 28, 449–454.CrossRefGoogle Scholar
McComb, W.D., Berera, A., Yoffe, S.R. & Linkmann, M. 2014 Energy transfer and dissipation in forced isotropic turbulence. Phys. Rev. E 91, 043013.CrossRefGoogle Scholar
McComb, W.D. & Fairhurst, R.B. 2018 The dimensionless dissipation rate and the Kolmogorov (1941) hypothesis of local stationarity in freely decaying isotropic turbulence. J. Math. Phys. 59, 073103.CrossRefGoogle Scholar
Meldi, M., Sagaut, P. & Lucor, D. 2011 A stochastic view of isotropic turbulence decay. J. Fluid Mech. 668, 351–362.CrossRefGoogle Scholar
Neitzel, G.P. 1982 Marginal stability of impulsively initiated Couette flow and spin-decay. Phys. Fluids 25, 226–232.CrossRefGoogle Scholar
Neitzel, G.P. & Davis, S.H. 1981 Centrifugal instabilities during spin-down to rest in finite cylinders. Numerical experiments. J. Fluid Mech. 102, 329–352.CrossRefGoogle Scholar
Ostilla-Mónico, R., Zhu, X., Spandan, V., Verzicco, R. & Lohse, D. 2017 Life stages of wall-bounded decay of Taylor–Couette turbulence. Phys. Rev. Fluids 2, 114601.CrossRefGoogle Scholar
Peixinho, J. & Mullin, T. 2006 Decay of turbulence in pipe flow. Phys. Rev. Lett. 96, 094501.CrossRefGoogle ScholarPubMed
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Rayleigh, O.M. 1917 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–154.Google Scholar
Saffman, P.G. 1967 The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27, 581–593.CrossRefGoogle Scholar
Savas, Ö. 1992 Spin-down to rest in a cylindrical cavity. J. Fluid Mech. 234, 529–552.CrossRefGoogle Scholar
Schikarski, T. & Avila, M. 2017 T mixer a novel system to investigate decaying turbulence in a wall-bounded environment. In 16th European Turbulence Conference.Google Scholar
Schneider, K. & Farge, M. 2008 Final states of decaying 2D turbulence in bounded domains: influence of the geometry. Physica D 237, 2228–2233.CrossRefGoogle Scholar
Singh, H. 2016 Particle image velocimetry and computational fluid dynamics applied to study the effect of hydrodynamics forces on animal cells cultivated in Taylor vortex bioreactor. PhD thesis, Universidade Federal do São Carlor – UFSCar.Google Scholar
Singh, H., Fletcher, D.F. & Nijdam, J.J. 2011 An assessment of different turbulence models for predicting flow in a baffled tank stirred with a Rushton turbine. Chem. Engng Sci. 66, 5976–5988.CrossRefGoogle Scholar
Sinhuber, M., Bodenschatz, E. & Bewley, G.P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114, 034501.CrossRefGoogle ScholarPubMed
Skrbek, L. & Stalp, S.R. 2000 On the decay of homogeneous isotropic turbulence. Phys. Fluids 12, 1997–2019.CrossRefGoogle Scholar
Sreenivasan, K.R. 1984 On the scaling of the turbulence energy dissipation rate. Phys. Fluids 27, 1048–1059.CrossRefGoogle Scholar
Taylor, G.I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421–444.Google Scholar
Thormann, A. & Maneveau, C. 2014 Decay of homogeneous, nearly isotropic turbulence behind active fractal grids. Phys. Fluids 26, 025112.CrossRefGoogle Scholar
Tillmann, W. 1967 Development of turbulence during the build-up of a boundary layer at a concave wall. Phys. Fluids 10, S108.CrossRefGoogle Scholar
Touil, H., Bertoglio, J.-P. & Shao, L. 2002 The decay of turbulence in a bounded domain. J. Turbul. 3, N49.CrossRefGoogle Scholar
Valente, P.C. & Vassilicos, J.C. 2015 The energy cascade in grid-generated non-equilibrium decaying turbulence. Phys. Fluids 27, 045103.CrossRefGoogle Scholar
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95–114.CrossRefGoogle Scholar
Verschoof, R.A., Huisman, S.G., van der Veen, R.C.A., Sun, C. & Lohse, D. 2016 Self-similar decay of high Reynolds number Taylor–Couette turbulence. Phys. Rev. Fluids 1, 062402.CrossRefGoogle Scholar

Singh and Prigent supplementary movie

Binarized movie presenting growth of vortical structures for Reynolds number $Re_o=1700$ over the whole axial height.

Download Singh and Prigent supplementary movie(Video)
Video 9.9 MB