Instability of Inelastic Shear-Thinning Liquids in a Couette Flow Between Concentric Cylinders

Abstract

Circular Couette flow of inelastic shear-thinning materials in annuli is examined. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the processes at which this type of flow occurs. Therefore, it is quite important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (dilute polymeric solutions) liquids. In this work, the effect of the shear-thinning behavior of high concentration suspensions on the onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and searching for the critical conditions. This procedure avoids the need for a stability analysis of the flow and the solution of an eigenproblem. The differential equations were solved by the Galerkin/finite-element method and the resulting set of nonlinear algebraic equations, by Newton’s method.

Effect of nonlinearity on the Taylor-Couette flow in the narrow-gap

“…Applying the low-order dynamics gives rise to the bifurcation diagram describing the full dynamic response of the system. In comparison with the only available study spotting only one critical point on the bifurcation diagram [21], the present study lays out the complete dynamical map of the nonlinear system. Also, several researches have attempted to carry out the stability analysis using classical turbulence models based on stochastic approach such as direct numerical simulation, DNS [22].…”

Taylor-Couette Instability of Giesekus Fluids: Inertia Effects

“…[9][10][11] On the other hand, from perturbation results obtained using "second-order" rheological model, the effect of a fluid's elasticity is known to be destabilizing.…”

“…[20][21][22][23] In the works cited above, simple viscoelastic models such as second-order, Maxwell, and Oldroyd-B have been used in the simulations. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] There are also works relying on more robust viscoelastic models such as Doi-Edwards, Giesekus, and FENE-P. [24][25][26] One can notably mention the numerical work carried out by Beris 26) in which the critical Taylor number has been calculated for the Giesekus fluid model-a rheological model known to be very good for representing polymeric liquids. Beris' study 26) was limited to the smallgap situation.…”

Flow pattern and stability of pseudoplastic axial Taylor–Couette flow

“…Applying the loworder dynamics gives rise to the bifurcation diagram describing the full dynamic response of the system. In comparison with the only available study spotting only one critical point on the bifurcation diagram [28], the present study lays out the complete dynamical map of the nonlinear system. Moreover, several researches have attempted to carry out the stability analysis using classical turbulence models based on stochastic approach such as direct numerical simulation, DNS [29].…”