Journal of Fluid Mechanics

Papers

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

Iman Lashgaria1, Jan O. Pralitsa2a3, Flavio Giannettia2 and Luca Brandta1 c1

a1 Linné Flow Centre, KTH Mechanics, S-100 44 Stockholm, Sweden

a2 DIIN, University of Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy

a3 DICAT, University of Genova, via Montallegro 1, 16145 Genova, Italy

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 $0. 4\leq n\leq 1. 75$ and $0. 1\leq \lambda \leq 100$. 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.

(Received October 31 2011)

(Reviewed February 09 2012)

(Accepted March 19 2012)

(Online publication April 30 2012)

Key Words:

  • instability;
  • non-Newtonian flows;
  • wakes

Correspondence:

c1 Email address for correspondence: luca@mech.kth.se

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