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

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<n<1.75 and 1<lambda<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

Shear rate projection schemes for non-Newtonian fluids

“…• The second test is the simulation of a flow past a cylinder of a Carreau fluid for various values of the power index [32]. Here the drag and wake (or re-circulation) lenght will be the object of comparison.…”

“…Reference solutions will be computed using a steady state mixed algorithm (denoted SS-Mix) based on a penalty method inside a fixed point loop for the viscosity. The data for the tests are taken from [32,34], adding another point of comparison. We can summarize the parameters as follow:…”

“…Finally, contrary to [32,33], a natural (or open) boundary condition is applied on Γ o . As an unconfined flow is modeled, and considering the open boundary condition, the outer boundary of the domain need to be sufficiently far from the cylinder so that boundary effects are at a minimum.…”

Global stability and control of the confined turbulent flow past a thick flat plate

“…[6][7][8][9] Within this framework, the concept of structural sensitivity has gained interest with applications to a large variety of globally unstable flows. [10][11][12][13][14][15] Indeed this linearised approach allows one to predict, beforehand, the effective positioning of a flow disturbance, i.e., a passive device, able to shift the vortex-shedding frequency or even to completely suppress the global instability of the flow. A remarkable example is represented by the possibility to qualitatively recover the well-known experimental control map of a) Author to whom correspondence should be addressed.…”

Non-similar Blasius and Sakiadis flow of a non-Newtonian Carreau fluid

“…Carreau [3] introduced a successful model which is used extensively up to date. Since then the Carreau model has been used to simulate non-Newtonian flows around spheres [4][5][6], over cylinders [7][8][9], in cavities [10,11], in pipes [12], in channels [13][14][15][16] and in intestines [17] to mention just a few of them. After an intensive investigation made in the literature no simulation has been found concerning the flow of a Carreau fluid over a stationary (Blasius) or moving surface (Sakiadis) flow which are two fundamental flows in fluid mechanics and this is the target of the present work.…”