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.

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.

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.

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-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.

Annular Frictional Pressure Losses During Drilling—Predicting the Effect of Drillstring Rotation

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Arild Saasen
Keyword(s):  
Rheological Properties ◽  
Pressure Loss ◽  
Drilling Fluid ◽  
Axial Flow ◽  
Drilling Fluids ◽  
Unstable Flow ◽  
Pressure Losses ◽  
Shear Dependent Viscosity ◽  
Water Based ◽  
Dependent Viscosity

Controlling the annular frictional pressure losses is important in order to drill safely with overpressure without fracturing the formation. To predict these pressure losses, however, is not straightforward. First of all, the pressure losses depend on the annulus eccentricity. Moving the drillstring to the wall generates a wider flow channel in part of the annulus which reduces the frictional pressure losses significantly. The drillstring motion itself also affects the pressure loss significantly. The drillstring rotation, even for fairly small rotation rates, creates unstable flow and sometimes turbulence in the annulus even without axial flow. Transversal motion of the drillstring creates vortices that destabilize the flow. Consequently, the annular frictional pressure loss is increased even though the drilling fluid becomes thinner because of added shear rate. Naturally, the rheological properties of the drilling fluid play an important role. These rheological properties include more properties than the viscosity as measured by API procedures. It is impossible to use the same frictional pressure loss model for water based and oil based drilling fluids even if their viscosity profile is equal because of the different ways these fluids build viscosity. Water based drilling fluids are normally constructed as a polymer solution while the oil based are combinations of emulsions and dispersions. Furthermore, within both water based and oil based drilling fluids there are functional differences. These differences may be sufficiently large to require different models for two water based drilling fluids built with different types of polymers. In addition to these phenomena washouts and tool joints will create localised pressure losses. These localised pressure losses will again be coupled with the rheological properties of the drilling fluids. In this paper, all the above mentioned phenomena and their consequences for annular pressure losses will be discussed in detail. North Sea field data is used as an example. It is not straightforward to build general annular pressure loss models. This argument is based on flow stability analysis and the consequences of using drilling fluids with different rheological properties. These different rheological properties include shear dependent viscosity, elongational viscosity and other viscoelastic properties.

STEADY FLOW OF FLUIDS WITH SHEAR-DEPENDENT VISCOSITY UNDER MIXED BOUNDARY VALUE CONDITIONS IN POLYHEDRAL DOMAINS

2000 ◽  
Vol 10 (05) ◽  
pp. 629-650 ◽  
Author(s):  
C. EBMEYER
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Steady Flow ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Partial Differential ◽  
Shear Dependent Viscosity ◽  
Polyhedral Domain ◽  
Dependent Viscosity

In this paper the system of partial differential equations [Formula: see text] is studied, where e is the symmetrized gradient of u, and T has p-structure for some p<2 (e.g. div T is the p-Laplacian and p<2). Mixed boundary value conditions on a three-dimensional polyhedral domain are considered. Ws,p-regularity (s=3/2-ε) of the velocity u and Wr,p′-regularity of the pressure π are proven.

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.

Relaxation Methods Applied to Two Problems of Two-Dimensional Stress Distribution Involving Mixed Boundary Conditions

1948 ◽  
Vol 1 (2) ◽  
pp. 135
Author(s):  
WH Wittrick ◽  
W Howard
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Stress Distributions ◽  
Relaxation Methods

Relaxation methods have been used to determine the stress distributions in both a rectangular and a highly tapered plate under tension when the load is applied through absolutely rigid clamps. Both problems require the treatment of boundary conditions involving the values of both stresses and displacements. The solutions were obtained in terms of displacements and the stresses were subsequently determined from them.

Sign in / Sign up

Export Citation Format

Share Document