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

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 i...

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Bibliographic Details
Published in:Journal of fluid mechanics 2012-06, Vol.701, p.201-227
Main Authors: Lashgari, Iman, Pralits, Jan O., Giannetti, Flavio, Brandt, Luca
Format: Article
Language:English
Subjects:
Base flow
Circular cylinders
Computational fluid dynamics
Exact sciences and technology
Fluid dynamics
Fluid flow
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Instability
Kinetic energy
Kinetics
Mathematical models
non-Newtonian flows
Non-newtonian fluid flows
Nonlinearity (including bifurcation theory)
Physics
Sensitivity analysis
Stability
Thinning
Viscosity
wakes
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Summary: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.
ISSN:0022-1120
1469-7645
1469-7645
DOI:10.1017/jfm.2012.151