Numerical experiments on the stability of unsteady circular Couette flow with random forcing

1987 ◽  
Vol 30 (5) ◽  
pp. 1250 ◽  
Author(s):  
J.-C. Chen ◽  
G. P. Neitzel ◽  
D. F. Jankowski
Keyword(s):  
Couette Flow ◽  
Numerical Experiments ◽  
Circular Couette Flow ◽  
Random Forcing ◽  
The Stability

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

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 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.

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.

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