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Experimental investigation of mixing and axial dispersion in Taylor–Couette flow patterns

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Abstract

The flow and mixing in a Taylor–Couette device have been characterized by means of simultaneous particle image velocimetry and planar laser-induced fluorescence (PLIF) measurements. Concentration of a passive tracer measurements was used to investigate mixing efficiency for different flow patterns (from steady Taylor vortex flow to modulated wavy vortex flow, MWVF). Taylor–Couette flow is known to evolve toward turbulence through a sequence of flow instabilities. Macroscopic quantities, such as axial dispersion and mixing index, are extremely sensitive to internal flow structures. PLIF measurements show clear evidences of different transport mechanisms including intravortex mixing and tracer fluxes through neighboring vortices. Under WVF and MWVF regimes, intravortex mixing is controlled by chaotic advection, due to the 3D nature of the flow, while intervortex transport occurs due to the presence of waves between neighboring vortices. The combination of these two mechanisms results in enhanced axial dispersion. We show that hysteresis may occur between consecutive regimes depending on flow history, and this may have a significant effect on mixing for a given Reynolds number.

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Abbreviations

c :

Critical

i :

Inner cylinder

e :

Outer cylinder

r :

Radial direction

θ :

Azimuthal direction

x :

Axial direction

\(r-x\) :

Meridional plane

0:

Initial condition

A :

Area of pixels with value 1 (−)

C :

Concentration (−)

\(\overline{C}\) :

Mean concentration (−)

\(C_{0}\) :

Injection concentration (g L−1)

\(C_{f}\) :

Final concentration (−)

\(D_{x}\) :

Dispersion coefficient (m2 s−1)

da :

Instantaneous area (m2)

dA :

Reference area (m2)

e :

Annular gap width (m)

f :

Frequency (s−1)

\(f_{\rm WVF}\) :

Traveling wave frequency (s−1)

F :

Spectral density of the gray level (−)

I :

Intensity of segregation (−)

\(I_{rx}\) :

Intensity of segregation in (−) the meridional plane (\(r-x\))

\(I_{\theta }\) :

Intensity of segregation in (−) the azimuthal direction (θ)

\(I_{v}\) :

Intensity of segregation (−) between adjacent vortices

L :

Column height (m)

m :

Azimuthal wave number (−)

\(m_{\rm inflow}\) :

Azimuthal wave number in inflow zone (−)

\(m_{\rm outflow}\) :

Azimuthal wave number in outflow zone

\(n_D\) :

Refraction index (−)

R :

Radius (m)

Re :

Reynolds number (−)

s :

Area stretch (−)

\(S_{a}\) :

Rate of stretching (s−1)

\(s_{i}\) :

Vortex size (m2)

S :

Taylor-cell size (m2)

t :

Time (s)

\(t_{\rm acc}\) :

Acceleration time (s)

\(T_{c}\) :

Inner cylinder rotational period (s)

\(T_{d}\) :

Vortex center rotational period (s)

U :

Velocity (m s−1)

\(V_{\phi }\) :

Phase velocity (rad s−1)

λ :

Wavelength (m)

\(\lambda _{x}\) :

Axial wavelength (m)

\(\sigma _{c}\) :

Standard deviation of concentration (−)

\(\sigma _{0}\) :

Mean max deviation (−)

η :

Radius ratio (−)

μ :

Dynamic viscosity (Pa s)

\(\nu\) :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

\(\varGamma\) :

Column aspect ratio (−)

\(\varOmega\) :

Inner cylinder rotational speed (s−1)

\(\varPhi\) :

Phase shift (−)

RTD:

Residence time distribution

PIV:

Particle image velocimetry

PLIF:

Planar laser-induced fluorescence

TVF:

Taylor vortex flow

WVF:

Wavy vortex flow

MWVF:

Modulated wavy vortex flow

TTVF:

Turbulent Taylor vortex flow

WIB:

Wavy inflow boundary

WOB:

Wavy outflow boundary

References

  • Akonur A, Lueptow R (2002) Chaotic mixing and transport in wavy Taylor–Couette flow. Phys D 167:183–196

    Article  MATH  Google Scholar 

  • Andereck D, Liu SS, Swinney HL (1985) Flow regimes in a circular Couette system with independently rotating cylinders. J Fluid Mech 164:155–183

    Article  Google Scholar 

  • Campero RJ, Vigil RD (1997) Axial dispersion during low Reynolds number Taylor–Couette flow: intra vortex mixing effect. Chem Eng J 52:3305–3310

    Google Scholar 

  • Coles D (1965) Transitions in circular Couette flow. J Fluid Mech 21:385–425

    Article  MATH  Google Scholar 

  • Davis MW, Weber EJ (1960) Liquid–liquid extraction between rotating concentric cylinders. Ind Eng Chem 52(11):929–934

    Article  Google Scholar 

  • Desmet G, Verelst H, Baron GV (1996) Local and global dispersion effect in Couette–Taylor flow—i. Description and modeling of the dispersion effects. Chem Eng J 51:1287–1298

    Article  Google Scholar 

  • Desmet G, Verelst H, Baron GV (1996b) Local and global dispersion effect in Couette–Taylor flow—ii. Quantative measurements and discussion of the reactor performance. Chem Eng J 51:1299–1309

    Article  Google Scholar 

  • Dusting J, Balabani S (2009) Mixing in Taylor–Couette reactor in the non wavy flow regime. Chem Eng Sci 64:3103–3111

    Article  Google Scholar 

  • Dutcher CS, Muller SJ (2009) Spatio-temporel mode dynamics and higher order transitions in high aspect ratio Newtonian Taylor–Couette flow. J Fluid Mech 641:85–113

    Article  MATH  Google Scholar 

  • Fenstermacher PR, Swinney HL, Gollub JP (1979) Dynamical instabilities and the transition to chaotic Taylor vortex flow. J Fluid Mech 94:103–127

    Article  Google Scholar 

  • Haut B, Amor HB, Coulon L, Jacquet A, Halloin V (2003) Hydrodynamics and mass transfer in a Couette–Taylor bioreactor for the culture of animal cells. Chem Eng J 58:777–784

    Article  Google Scholar 

  • Hill E, Krebs B, Goodall D, Howlett G, Dunstan D (2006) Shear flow induces amyloid fibril formation. Biomacromolecules 7:10–13

    Article  Google Scholar 

  • Imomoh E, Dusting J, Balabani S (2010) On the quasiperiodic state in a moderate aspect ratio Taylor–Couette flow. Phys Fluids 22:044103

  • Kataoka K, Hongo T, Fugatawa M (1975) Ideal plug-flow properties of Taylor-vortex flow. J Chem Eng Japan 8:472–476

    Article  Google Scholar 

  • Kataoka K, Doi H, Komai T (1977) Heat and mass transfer in Taylor-vortex flow with constant axial flow rate. Int J Heat Mass Transf 57:472–476

    Google Scholar 

  • Kataoka K, Takigawa T (1981) Intermixing over cell boundary between Taylor vortices. AIChE J 27:504–508

    Article  Google Scholar 

  • Kataoka K, Ohmura N, Kouzu M, Simamura Y, Okubu M (1995) Emulsion polymerization of styrene in a continuous Taylor vortex flow reactor. Chem Eng Sci 50:1409–1416

    Article  Google Scholar 

  • King GP, Rowlands G, Rudman M, Yannacopoulos AN (2001) Predicting chaotic dispersion with Eulerian measures: wavy Taylor vortex flow. Phys Fluids 13:2522

    Article  MathSciNet  Google Scholar 

  • Legrand J, Coeuret F (1986) Circumferentional mixing in one phase and two-phase Taylor vortex flow. Chem Eng J 41:47–53

    Article  Google Scholar 

  • Moore C, Cooney C (1995) Axial dispersion in Taylor–Couette flow. AIChE J 41:723–727

    Article  Google Scholar 

  • Nemri M, Charton S, Climent E, Lanoe JY (2012) Experimental and numerical investigation on mixing and axial dispersion in Taylor–Couette flow patterns. Chem Eng Res Des 91:2346–2354

    Article  Google Scholar 

  • Ohmura N, Kataoka K, Shibata Y, Makino T (1997a) Effective mass diffusion over cell boundaries in Taylor–Couette flow system. Chem Eng J 52(11):1757–1765

    Article  Google Scholar 

  • Ohmura N, Makino T, Motomura A, Shibata Y, Kataoka K, Makino T (1997b) Intercellular mass transfer in waving/turbulent Taylor vortex flow. Int J Heat Fluid Flow 19:159–166

    Article  Google Scholar 

  • Ottino JM (1989) The kinematics of mixing: stretching, chaos and transport. The Press Syndicate of the University of Cambridge, Cambridge

    MATH  Google Scholar 

  • Pudijioni PI, Tavare NS, Garside J, Nigam KDP (1992) Residence time distribution from a continuous Couette flow device. Chem Eng J 48:101–110

    Article  Google Scholar 

  • Rudman M (1998) Mixing and particle dispersion in the wavy vortex regime of Taylor–Couette flow. AIChE J 44(5):1015–1026

    Article  Google Scholar 

  • Rudman M, Metcalfe G, Lachlan J, Graham W (2008) Nonmixing vortex cores in wavy Taylor vortex flow. Phys Fluids 20:063602

  • Sakakibara J, Hishida K, Maeda M (1993) Measurements of thermally stratified pipe flow using image-processing techniques. Exp Fluids 16:82–96

    Article  Google Scholar 

  • Tam WY, Swinney HL (1987) Mass transport in turbulent Taylor–Couette flow. Phys Rev A 36:1374–1381

    Article  Google Scholar 

  • Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc Lond 223:289–343

    Article  MATH  Google Scholar 

  • Wereley ST, Lueptow RM (1999) Velocity field for Taylor–Couette flow with an axial flow. Phys Fluids 11(12):3637–3649

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank M. Marchal, from IMFT, and F. Lamadie, from CEA Marcoule, for experimental support and fruitful discussions.

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Authors and Affiliations

  1. CEA, DEN, DTEC, SGCS, 30207, Bagnols-sur-Cèze, France

    Marouan Nemri & Sophie Charton

  2. Institut de Mécanique des Fluides de Toulouse (IMFT), CNRS, Université de Toulouse, Allée Camille Soula, 31400, Toulouse, France

    Sébastien Cazin & Eric Climent

Authors
  1. Marouan Nemri
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  2. Sébastien Cazin
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  3. Sophie Charton
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  4. Eric Climent
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Correspondence to Eric Climent.

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Nemri, M., Cazin, S., Charton, S. et al. Experimental investigation of mixing and axial dispersion in Taylor–Couette flow patterns. Exp Fluids 55, 1769 (2014). https://doi.org/10.1007/s00348-014-1769-6

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  • DOI: https://doi.org/10.1007/s00348-014-1769-6

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