Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 9
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Pantokratoras, Asterios 2015. Non-similar Blasius and Sakiadis flow of a non-Newtonian Carreau fluid. Journal of the Taiwan Institute of Chemical Engineers, Vol. 56, p. 1.


    Govindarajan, Rama and Sahu, Kirti Chandra 2014. Instabilities in Viscosity-Stratified Flow. Annual Review of Fluid Mechanics, Vol. 46, Issue. 1, p. 331.


    Pantokratoras, Asterios 2016. Steady flow of a non-Newtonian Carreau fluid across an unconfined circular cylinder. Meccanica, Vol. 51, Issue. 4, p. 1007.


    Carini, M. Giannetti, F. and Auteri, F. 2014. On the origin of the flip–flop instability of two side-by-side cylinder wakes. Journal of Fluid Mechanics, Vol. 742, p. 552.


    Luchini, Paolo and Bottaro, Alessandro 2014. Adjoint Equations in Stability Analysis. Annual Review of Fluid Mechanics, Vol. 46, Issue. 1, p. 493.


    Camarri, Simone 2015. Flow control design inspired by linear stability analysis. Acta Mechanica, Vol. 226, Issue. 4, p. 979.


    Carini, M. Giannetti, F. and Auteri, F. 2014. First instability and structural sensitivity of the flow past two side-by-side cylinders. Journal of Fluid Mechanics, Vol. 749, p. 627.


    Citro, Vincenzo Giannetti, Flavio and Pralits, Jan O 2015. Three-dimensional stability, receptivity and sensitivity of non-Newtonian flows inside open cavities. Fluid Dynamics Research, Vol. 47, Issue. 1, p. 015503.


    Griffiths, P. T. Gallagher, M. T. and Stephen, S. O. 2016. The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer. Physics of Fluids, Vol. 28, Issue. 7, p. 074107.


    ×
  • Journal of Fluid Mechanics, Volume 701
  • June 2012, pp. 201-227

First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder

  • Iman Lashgari (a1), Jan O. Pralits (a2) (a3), Flavio Giannetti (a2) and Luca Brandt (a1)
  • DOI: http://dx.doi.org/10.1017/jfm.2012.151
  • Published online: 30 April 2012
Abstract
Abstract

The first bifurcation and the instability mechanisms of shear-thinning and shear-thickening fluids flowing past a circular cylinder are studied using linear theory and numerical simulations. Structural sensitivity analysis based on the idea of a ‘wavemaker’ is performed to identify the core of the instability. The shear-dependent viscosity is modelled by the Carreau model where the rheological parameters, i.e. the power-index and the material time constant, are chosen in the range and . We show how shear-thinning/shear-thickening effects destabilize/stabilize the flow dramatically when scaling the problem with the reference zero-shear-rate viscosity. These variations are explained by modifications of the steady base flow due to the shear-dependent viscosity; the instability mechanisms are only slightly changed. The characteristics of the base flow, drag coefficient and size of recirculation bubble are presented to assess shear-thinning effects. We demonstrate that at critical conditions the local Reynolds number in the core of the instability is around 50 as for Newtonian fluids. The perturbation kinetic energy budget is also considered to examine the physical mechanism of the instability.

Copyright
Corresponding author
Email address for correspondence: luca@mech.kth.se
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.F. Alizard , J.-C. Robinet & U. Rist 2010 Sensitivity analysis of a streamwise corner flow. Phys. Fluids 22 (1), 014103.






8.F. Caton 2006 Linear stability of circular Couette flow of inelastic viscoplastic fluids. J. Non-Newtonian Fluid Mech. 134, 148154.

9.J.-M. Chomaz 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.

10.P. M. Coelho & F. T. Pinho 2003a Vortex shedding in cylinder flow of shear-thinning fluids. I identification and demarcation of flow regimes. J. Non-Newtonian Fluid Mech. 110, 143176.

12.P. M. Coelho & F. T. Pinho 2004 Vortex shedding in cylinder flow of shear-thinning fluids. III pressure measurements. J. Non-Newtonian Fluid Mech. 121, 5568.

13.P. F. Fischer & E. M. Rønquist 1994 Spectral element methods for large scale parallel Navier–Stokes calculations. Comput. Meth. Appl. Mech. Engng 116, 6976.




19.P. Meliga , D. Sipp & J.-M. Chomaz 2010b Open-loop control of compressible afterbody flows using adjoint methods. Phys. Fluids 22 (5), 054109.

20.S. Milleta , F. Rousset & V. B. H. B. Hadid 2009 Stability analysis of stratified coating flow of shear-thinning fluids. Eur. Phys. J. Special Topics 166, 143146.

21.S. Mossaz , P. Jay & A. Magnin 2010 Criteria for the appearance of recirculating and non-stationary regimes behind a cylinder in a viscoplastic fluid. J. Non-Newtonian Fluid Mech. 165, 15251535.

22.A. Nejat , V. Abdollahi & K. Vahidkhah 2011 Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders. J. Non-Newtonian Fluid Mech. 166, 689697.


24.C. Nouar & I. Frigaard 2009 Stability of plane Couette-Poiseuille flow of shear-thinning fluid. Phys. Fluids 21, 064104.

25.S. K. Panda & R. Chhabra 2010 Laminar flow of power-law fluids past a rotating cylinder. J. Non-Newtonian Fluid 165, 14421461.

26.A. T. Patera 1984 A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54, 468488.

27.V. K. Patnana , R. P. Bharti & R. P. Chhabra 2009 Two-dimensional unsteady flow of power-law fluids over a cylinder. Chem. Engng Sci. 64, 29782999.

28.C. J. Pipe & P. A. Monkewitz 2006 Vortex shedding in flows of dilute polymer solutions. J. Non-Newtonian Fluid Mech. 139, 5467.



32.D. Richter , E. S. G. Shaqfeh & G. Iaccarino 2011 Floquet stability analysis of viscoelastic flow over a cylinder. J. Non-Newtonian Fluid Mech. 166, 554565.


34.D. Sipp , O. Marquet , P. Meliga & A. Barbagallo 2010 Dynamics and control of global instabilities in open flows: a linearized approach. Appl. Mech. Rev. 63, 030801.

35.P. Sivakumar , R. P. Bharti & R. Chhabra 2006 Effect of power-law index on critical parameters for power-law flow across an unconfined circular cylinder. Chem. Engng Sci. 61, 60356046.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: