Stability of Shear-Thickening Liquids Between Rotating Cylinders

2010 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

Shear-Thickening Flow Between Coaxial Cylinders

2011 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow; however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

Stability of Shear-Thinning Flow Between Rotating Cylinders

2007 ◽  
Author(s):  
Nariman Ashrafi
Keyword(s):  
Couette Flow ◽  
Shear Thinning ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
The Stability ◽  
Dependent Viscosity ◽  
Exchange Of Stability ◽  
Thinning Effect

The effect of shear thinning on the stability of the Taylor-Couette flow (TCF) is explored for a Carreau-Bird fluid in the narrow-gap limit to simulate shear-dependent viscosity of lubricants. Here, a low-order dynamical system is obtained from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow becomes lower s the shear-thinning effect increases. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a second critical value. At this point, A Hopf bifurcation emerges, which exists only for shear-thinning fluids.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

Effects of Shear Thinning on Taylor-Couette Flow: A Model for Synovial Fluid Flow

2006 ◽  
Author(s):  
Nariman Ashrafi
Keyword(s):  
Couette Flow ◽  
Shear Thinning ◽  
Taylor Number ◽  
Taylor Vortex ◽  
Narrow Gap ◽  
Shear Thinning Fluids ◽  
Wide Range ◽  
Taylor Couette ◽  
The Stability ◽  
Taylor Couette Flow

The effect of shear thinning on the stability of the Taylor-Couette flow (TCF) is explored for a Carreau-Bird fluid in the narrow-gap limit to simulate journal bearings in general. Also considered is the changing eccentricity to cover a wide range of applied situations such as bearings and even articulation of human joints. Here, a low-order dynamical system is obtained from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow becomes lower s the shear-thinning effect increases. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, A Hopf bifurcation emerges, which exists only for shear-thinning fluids. Variation of stresses in the narrow gap has been evaluated with significant applications in the non-Newtonian lubricant.

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

2012 ◽  
Vol 701 ◽  
pp. 201-227 ◽  
Author(s):  
Iman Lashgari ◽  
Jan O. Pralits ◽  
Flavio Giannetti ◽  
Luca Brandt
Keyword(s):  
Circular Cylinder ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Base Flow ◽  
Rheological Parameters ◽  
Recirculation Bubble ◽  
The Core ◽  
Shear Dependent Viscosity ◽  
Shear Thickening Fluids ◽  
Dependent Viscosity

AbstractThe 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.

Revisiting the stability of circular Couette flow of shear-thinning fluids

2012 ◽  
Vol 183-184 ◽  
pp. 37-51 ◽  
Author(s):  
Brahim Alibenyahia ◽  
Cécile Lemaitre ◽  
Chérif Nouar ◽  
Noureddine Ait-Messaoudene
Keyword(s):  
Couette Flow ◽  
Shear Thinning ◽  
Circular Couette Flow ◽  
Shear Thinning Fluids ◽  
The Stability

scholarly journals Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

2021 ◽  
Vol 933 ◽  
Author(s):  
S. Topayev ◽  
C. Nouar ◽  
J. Dusek
Keyword(s):  
Numerical Simulations ◽  
Couette Flow ◽  
Vortex Flow ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Thinning Fluids ◽  
Taylor Vortex Flow ◽  
Viscous Shear ◽  
Taylor Couette ◽  
Shear Thinning Fluid

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is $\eta = R_1/R_2=0.4$ . The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at ${Re} = 5.28 \, {Re}_c$ . At ${Re} = 6.9 \, {Re}_c$ , the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

Formation of Boundary Layer in the Flow of Shear-Dependent-Viscosity Fluids Between Parallel Plates

2017 ◽  
Author(s):  
Nariman Ashrafi ◽  
Ali Sadeghi ◽  
Mehdi Shafahi
Keyword(s):  
Boundary Layer ◽  
Flow Behavior ◽  
Vertical Wall ◽  
Shear Thickening ◽  
Finite Volume Scheme ◽  
Parallel Plates ◽  
Flow Behavior Index ◽  
Shear Dependent Viscosity ◽  
Shear Thickening Fluids ◽  
Dependent Viscosity

Formation of the boundary layer in the laminar flow of Herschel–Bulkley fluid between parallel plates is taken into consideration. In particular, the study is focused on the flow of the shear thinning and shear thickening fluids past a partial vertical wall in between the plates. Upon numerically solving the continuity and momentum equations the flow is analyzed throughout the domain using a finite volume scheme. The shear stress at the wall together with velocity distribution are evaluated and compared with experimental results for several values of Herschel-Bulkley coefficients for fluidity and flow behavior index.

Two Dimensional Unsteady Laminar Flow of Power Law Fluids Past a Square Cylinder: A Numerical Study

2008 ◽  
Author(s):  
Akhilesh K. Sahu ◽  
Raj P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Shear Thickening ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
Edge Separation

The two-dimensional and unsteady flow of power-law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time for Newtonian fluids. However, no such information is available for power law fluids. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The macroscopic quantities such as drag coefficients, Strouhal number, lift coefficient as well as the detailed kinematic variables like stream function, vorticity and so on, have been calculated as functions of the pertinent dimension-less groups. In particular, the effects of Reynolds number and of the power-law index have been investigated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening behaviour delays the leading edge separation. So, the drag coefficient in the above-mentioned range of Reynolds number, Re, in shear-thinning fluids (n < 1) initially decreases but at high values of the Reynolds number, it increases. As expected, on the other hand, in case of shear-thickening fluids (n > 1) drag coefficient reduces with Reynolds number, Re. Furthermore, the present results also suggest the transition from steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thickening fluids than that in Newtonian fluids. Also, the spectra of lift signal for shear-thickening fluids show that the flow is truly periodic in nature with a single dominant frequency in the above range of Reynolds number. In shear-thinning fluids at higher Re, quasi-periodicity sets in with additional frequencies, which indicate the transition from the 2-D to 3-D flows.

A Liquid Metal Flow Between Two Coaxial Cylinders System

2019 ◽  
Vol 11 (1) ◽  
pp. 79-86
Author(s):  
Abdelkrim Merah ◽  
Ridha Kelaiaia ◽  
Faiza Mokhtari
Keyword(s):  
Couette Flow ◽  
Metal Flow ◽  
Three Dimensional ◽  
Liquid Sodium ◽  
Taylor Vortex ◽  
Turbulent Regime ◽  
Coaxial Cylinders ◽  
Concentric Cylinders ◽  
Ideal Tool ◽  
The Stability

Abstract The Taylor-Couette flow between two rotating coaxial cylinders remains an ideal tool for understanding the mechanism of the transition from laminar to turbulent regime in rotating flow for the scientific community. We present for different Taylor numbers a set of three-dimensional numerical investigations of the stability and transition from Couette flow to Taylor vortex regime of a viscous incompressible fluid (liquid sodium) between two concentric cylinders with the inner one rotating and the outer one at rest. We seek the onset of the first instability and we compare the obtained results for different velocity rates. We calculate the corresponding Taylor number in order to show its effect on flow patterns and pressure field.

Sign in / Sign up

Export Citation Format

Share Document