Stability of Non-Newtonian Taylor-Couette With Axial Flow

2011 ◽  
Author(s):  
N. Ashrafi ◽  
A. Hazbavi
Keyword(s):  
Bifurcation Diagram ◽  
Mixed Boundary ◽  
Axial Flow ◽  
Mixed Boundary Conditions ◽  
Shear Thinning ◽  
Base Flow ◽  
Taylor Number ◽  
Galerkin Projection ◽  
Shear Dependent Viscosity ◽  
Taylor Couette

The influence of axial flow on stability of the Taylor-Couette flow is carried for shear thinning fluids. The fluid is assumed to follow the Carreau-Bird model and mixed boundary conditions are imposed. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear thinning effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, shear-thinning Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, manifested by a pressure gradient appears to further advance each critical point on the bifurcation diagram. Complete flow field together with viscosity maps are given for different scenarios in the bifurcation diagram.

Effect of Axial Flow on Taylor-Couette Stability

2011 ◽  
Author(s):  
N. Ashrafi ◽  
A. Hazbavi
Keyword(s):  
Bifurcation Diagram ◽  
Mixed Boundary ◽  
Axial Flow ◽  
Mixed Boundary Conditions ◽  
Shear Thinning ◽  
Base Flow ◽  
Galerkin Projection ◽  
Stress Distributions ◽  
Shear Dependent Viscosity ◽  
Dependent Viscosity

Stability of the shear thinning flow between rotating coaxial cylinders with axial flow is carried out. The fluid is assumed to follow the Carreau-Bird model and mixed boundary conditions are imposed. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the shear thinning effects increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. Existence of an axial flow, manifested by a pressure gradient appears to further advance each critical point on the bifurcation diagram. Complete flow field together with viscosity maps and stress distributions are given for different scenarios in the bifurcation diagram.

Chaos in Non-Newtonian Rotational Flow With Axial Flow

2012 ◽  
Author(s):  
N. Ashrafi ◽  
A. Hazbavi ◽  
F. Forghani
Keyword(s):  
Transient Flow ◽  
Mixed Boundary ◽  
Vortex Formation ◽  
Axial Flow ◽  
Mixed Boundary Conditions ◽  
Base Flow ◽  
Taylor Number ◽  
Galerkin Projection ◽  
Rotating Flow ◽  
Shear Dependent Viscosity

The influence of axial flow on the vortex formation of pseudoplastic rotating flow between cylinders is explored. The fluid is assumed to follow the Carreau-Bird model and mixed boundary conditions are imposed. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the pseudoplasticity increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, manifested by a pressure gradient appears to further advance each critical point on the bifurcation diagram. In addition to the simulation of spiral flow, the proposed formulation allows the axial flow to be independent of the main rotating flow. Complete transient flow field together with viscosity maps are also presented.

Dynamical Analysis of Magnetorheological Rotational Flow

2011 ◽  
Author(s):  
Nariman Ashrafi ◽  
Abdolreza Mortezapoor
Keyword(s):  
Axial Magnetic Field ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Axial Direction ◽  
Base Flow ◽  
Taylor Number ◽  
Galerkin Projection ◽  
Dynamical Analysis ◽  
Rotational Flow ◽  
Magnetic Excitation

Stability of the magnetorheological rotational flow in presence of magnetic excitation in the axial direction is examined. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations while mixed boundary conditions are assumed. In absence of magnetic excitation, the base flow loses its radial flow stability to the vortex structure at a critical Taylor number. The emergence of the vortices corresponds to the onset of a supercritical bifurcation. The Taylor vortices, in turn, lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. The axial magnetic field turns out to be a controlling parameter as it alters the critical points throughout the bifurcation diagram.

Stability Analysis of Non-Newtonian Rotational Flow With Hydromagnetic Effect

2014 ◽  
Author(s):  
N. Ashrafi ◽  
A. Hazbavi
Keyword(s):  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Tangential Direction ◽  
Deborah Number ◽  
Base Flow ◽  
Taylor Number ◽  
Rotational Flow ◽  
Magnetic Excitation ◽  
Fluid Elasticity ◽  
Flow Parameters

Stability of the magnetorheological rotational flow in the presence of a magnetic excitation in the tangential direction is examined. The conservation of mass and momentum equations for an isothermal Carreau fluid between coaxial cylinders are numerically solved while mixed boundary conditions are assumed. In the absence of magnetic excitation, the base flow loses its radial flow stability to the vortex structure at a critical Taylor number. The emergence of the vortices corresponds to the onset of a supercritical bifurcation. The Taylor vortices, in turn, lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. The tangential magnetic field turns out to be a controlling parameter as it alters the critical points throughout the bifurcation diagram. Also, the effect of the Hartmann number, the Deborah number and the fluid elasticity on the flow parameters were investigated.

Experimental Investigations of the Surface Groove Effect in Taylor-Couette-Poiseuille Flow

2020 ◽  
Author(s):  
Lamia Gaied ◽  
Fethi Aloui ◽  
Marc Lippert ◽  
Emna Berrich
Keyword(s):  
Couette Flow ◽  
Vortex Flow ◽  
Axial Flow ◽  
Vortex Structures ◽  
Base Flow ◽  
Taylor Vortex ◽  
Experimental Investigations ◽  
Surface Groove ◽  
Taylor Couette ◽  
The Impact

Abstract In this paper, we investigate the effects of an imposed axial flow on hydrodynamic instabilities’ Couette-Taylor flow in the case where the wall of the inner cylinder of the system is grouved. Without imposed axial flow, the basic flow of a fluid between two coaxial cylinders known by Couette flow, which is characterized by several temporal and spatial symmetries. The increase in the rotation causes the breaking of these symmetries. In both cases where the surface of the inner cylinder is smooth and grooved, five different flow regimes can be determined: Taylor vortex flow (TVF), wavy vortex flow (WVF), and Modulated Wavy vortex flow (MWVF). Each time the flow passes from one hydrodynamic regime to another until it enters a state of turbulence, which is characterized by the destruction of all the symmetries that existed at the beginning. In addition, when an axial flow is imposed on a Taylor-Couette flow, new helical vortex structures are observed in both cases (with and without surface groove). The influence of surface structures (grooves) on the shear stress of the wall is discussed with and without axial base flow. A spatio-temporal description of several flow models was obtained using firstly, a visualization’s qualitative study using kalliroscope particles. Secondly, a quantitative study by polarography using simple probes have been used to characterize the impact of vortex structures on the Couette-Taylor flows without and with an axial flow on the transfer.

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.

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.

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