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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)

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.

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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.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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