scholarly journals Emergent order in rheoscopic swirls

2010 ◽  
Vol 667 ◽  
pp. 158-187 ◽  
Author(s):  
MICHAEL WILKINSON ◽  
VLAD BEZUGLYY ◽  
BERNHARD MEHLIG
Keyword(s):  
Order Parameter ◽  
Periodic Potential ◽  
Two Dimensional ◽  
One Dimensional ◽  
Emergent Order ◽  
Long Time ◽  
Parameter Field ◽  
Two Dimensional Flow ◽  
Reflection Of Light ◽  
Local Average

We consider the ordering of particles in a rheoscopic fluid (a suspension of microscopic rod-like particles) in a steady two-dimensional flow, and discuss its consequences for the reflection of light. The ordering is described by an order parameter which is a non-oriented vector, obtained by averaging solutions of a nonlinear equation containing the strain rate of the fluid flow. Exact solutions of this equation are obtained from solutions of a linear equation which are analogous to Bloch bands for a one-dimensional Schrödinger equation with a periodic potential. On some contours of the stream function, the order parameter approaches a limit, and on others it depends increasingly sensitively upon position. However, in the long-time limit a local average of the order parameter is a smooth function of position in both cases. We analyse the topology of the order parameter and the structure of the generic zeros of the order parameter field.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

scholarly journals A study of two-dimensional flow past an oscillating cylinder

1999 ◽  
Vol 385 ◽  
pp. 255-286 ◽  
Author(s):  
H. M. BLACKBURN ◽  
R. D. HENDERSON
Keyword(s):  
Experimental Studies ◽  
Cross Flow ◽  
Relaxation Oscillator ◽  
Two Dimensional ◽  
Flow State ◽  
Long Time ◽  
Two Dimensional Flow ◽  
Vorticity Production ◽  
Oscillation Frequencies ◽  
Motion Amplitude

In this paper we describe a detailed study of the wake structures and flow dynamics associated with simulated two-dimensional flows past a circular cylinder that is either stationary or in simple harmonic cross-flow oscillation. Results are examined for Re=500 and a fixed motion amplitude of ymax/D=0.25. The study concentrates on a domain of oscillation frequencies near the natural shedding frequency of the fixed cylinder. In addition to the change in phase of vortex shedding with respect to cylinder motion observed in previous experimental studies, we note a central band of frequencies for which the wake exhibits long-time-scale relaxation oscillator behaviour. Time-periodic states with asymmetric wake structures and non-zero mean lift were also observed for oscillation frequencies near the lower edge of the relaxation oscillator band. In this regime we compute a number of bifurcations between different wake configurations and show that the flow state is not a unique function of the oscillation frequency. Results are interpreted using an analysis of vorticity generation and transport in the base region of the cylinder. We suggest that the dynamics of the change in phase of shedding arise from a competition between two different mechanisms of vorticity production.

Circulation Generation and Vortex Ring Formation by Conic Nozzles

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Moshe Rosenfeld ◽  
Kakani Katija ◽  
John O. Dabiri
Keyword(s):  
Vortex Ring ◽  
Vortex Generator ◽  
Ring Formation ◽  
Vortex Rings ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Vortex Ring Formation ◽  
Exit Nozzle ◽  
Two Dimensional Flow

Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

Mathematical aspects of the theory of inviscid hypersonic flow

1991 ◽  
Vol 335 (1637) ◽  
pp. 121-138 ◽  
Keyword(s):  
Chemical Reactions ◽  
Mathematical Analysis ◽  
Solution Structure ◽  
Well Posedness ◽  
Two Dimensional ◽  
Open Problems ◽  
Real Gas ◽  
One Dimensional ◽  
Two Dimensional Flow ◽  
Real Gas Effects

This paper reviews some differential equations arising in the theory of inviscid hypersonic gasdynamics. The only real-gas effects that we have incorporated are simple models for chemical reactions. After describing what is known about the solution structure of these equations in unsteady one-dimensional and steady two- dimensional flow, we make some conjectures about the well-posedness and regularization of certain specific open problems which have not yet been susceptible to mathematical analysis.

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