Axial flow effects on the stability of circular Couette flow with viscous heating

2006 ◽  
Vol 18 (8) ◽  
pp. 084106
Author(s):  
David L. Cotrell ◽  
G. B. McFadden
Keyword(s):  
Couette Flow ◽  
Axial Flow ◽  
Viscous Heating ◽  
Circular Couette Flow ◽  
Flow Effects ◽  
The Stability

Effect of axial flow on viscoelastic Taylor–Couette instability

1998 ◽  
Vol 360 ◽  
pp. 341-374 ◽  
Author(s):  
M. D. GRAHAM
Keyword(s):  
Couette Flow ◽  
Poiseuille Flow ◽  
Axial Flow ◽  
Weissenberg Number ◽  
Scaling Analysis ◽  
Plane Shear ◽  
Weakly Nonlinear ◽  
Elastic Stresses ◽  
Circular Couette Flow ◽  
The Stability

Viscoelastic flow instabilities can arise from gradients in elastic stresses in flows with curved streamlines. Circular Couette flow displays the prototypical instability of this type, when the azimuthal Weissenberg number Weθ is O(ε−1/2), where ε measures the streamline curvature. We consider here the effect of superimposed steady axial Couette or Poiseuille flow on this instability. For inertialess flow of an upper-convected Maxwell or Oldroyd-B fluid in the narrow gap limit (ε[Lt ]1), the analysis predicts that the addition of a relatively weak steady axial Couette flow (axial Weissenberg number Wez=O(1)) can delay the onset of instability until Weθ is significantly higher than without axial flow. Weakly nonlinear analysis shows that these bifurcations are subcritical. The numerical results are consistent with a scaling analysis for Wez[Gt ]1, which shows that the critical azimuthal Weissenberg number for instability increases linearly with Wez. Non-axisymmetric disturbances are very strongly suppressed, becoming unstable only when ε1/2Weθ= O(We2z). A similar, but smaller, stabilizing effect occurs if steady axial Poiseuille flow is added. In this case, however, the bifurcations are converted from subcritical to supercritical as Wez increases. The observed stabilization is due to the axial stresses introduced by the axial flow, which overshadow the destabilizing hoop stress. If only a weak (Wez[les ]1) steady axial flow is added, the flow is actually slightly destabilized. The analysis also elucidates new aspects of the stability problems for plane shear flows, including the exact structure of the modes in the continuous spectrum, and illustrates the connection between these problems and the viscoelastic circular Couette flow.

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

The stability of plane Couette flow of a power-law fluid with viscous heating

2007 ◽  
Vol 19 (9) ◽  
pp. 094107 ◽  
Author(s):  
Nabil T. M. Eldabe ◽  
M. F. El-Sabbagh ◽  
M. A.-S. El-Sayed(Hajjaj)
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Viscous Heating ◽  
Plane Couette Flow ◽  
Power Law Fluid ◽  
The Stability

Energy stability of modulated circular Couette flow

1977 ◽  
Vol 79 (3) ◽  
pp. 535-552 ◽  
Author(s):  
Peter J. Riley ◽  
Robert L. Laurence
Keyword(s):  
Couette Flow ◽  
Nonlinear Stability ◽  
Energy Analysis ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Initial Energy ◽  
Critical Parameters ◽  
Narrow Gap ◽  
Circular Couette Flow ◽  
The Stability

The stability of circular Couette flow when the outer cylinder is at rest and the inner is modulated both with and without a mean shear is examined in the narrow-gap limit. Disturbances are assumed to be axisymmetric. Two criteria are used to determine conditions for stability; the first requires that the motion be strongly stable, the second only that disturbances of arbitrary initial energy decay from cycle to cycle. The behaviour of critical parameters as a function of frequency is similar for the linear and the energy analysis. The range of Reynolds numbers bounded above by certain instability and below by conditional nonlinear stability is enlarged by modulation.

The stability of plane Couette flow with viscous heating

1973 ◽  
Vol 57 (4) ◽  
pp. 651-670 ◽  
Author(s):  
Peter C. Sukanek ◽  
Charles A. Goldstein ◽  
Robert L. Laurence
Keyword(s):  
Couette Flow ◽  
Maximum Shear Stress ◽  
Negative Real Part ◽  
Navier Stokes ◽  
Exponential Dependence ◽  
Viscous Heating ◽  
Thermal Mode ◽  
Neutral Stability ◽  
Plane Couette Flow ◽  
The Stability

An investigation of the stability of plane Couette flow with viscous heating of a Navier–Stokes–Pourier fluid with an exponential dependence of viscosity upon temperature is presented. Using classical small perturbation theory, the stability of the flow can be described by a sixth-order set of coupled ordinary differential equations. Using Galerkin's method, these equations are reduced to an algebraic eigenvalue problem. An eigenvalue with a negative real part means that the flow is unstable.Neutral stability curves are determined at Brinkman numbers of 15, 19, 25, 30,40,80 and 600 for Prandtl numbers of 1, s and 50. A Brinkman number of 19 corresponds approximately to the maximum shear stress which can be applied to the system.The results indicate that four different modes of instability occur: one termed an inviscid mode, arising from an inflexion point in the primary flow; a viscous mode, due to the stratification of viscosity in the flow field and an associated diffusive mechanism; a coupling mode, resulting from the convective and viscous dissipation terms in the energy equation; and finally a purely thermal mode.

The Stability of Blood Cell Suspensions to Small Disturbances in Circular Couette Flow: Experimental Results for the Taylor Problem

1979 ◽  
Vol 101 (4) ◽  
pp. 289-292 ◽  
Author(s):  
S. Deutsch ◽  
W. M. Phillips
Keyword(s):  
Blood Cell ◽  
Blood Plasma ◽  
Couette Flow ◽  
Cell Suspensions ◽  
Experimental Results ◽  
Red Cell ◽  
Red Cell Deformability ◽  
Circular Couette Flow ◽  
The Stability ◽  
Small Disturbances

Experimental results for the stability of human blood, red cell suspensions and blood plasma to small disturbances in circular Couette flow are presented. The viscoelastic nature of whole blood and blood cell suspensions is confirmed. Blood plasma is found to be Newtonian. Elasticity is shown to have a sizably stabilizing effect on normal Hematocrit blood behavior. Two mechanisms by which elasticity may arise in blood are identified; namely red cell deformability and red cell aggregation.

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