In this research we study the mixing of viscous fluids in a model flow, the eccentric cylinder system. The flow between eccentric rotating cylinders is used because an analytic expression for the stream function exists and we have fabricated an apparatus to experimentally generate the flow. We use the flow to determine the extent to which several computational methods are able to predict the experimental mixing in the flow. We have found that Poincare sections give a good indication of the maximum extent of mixing in the experiments but they give no information on the rate of mixing. The locations of elliptic periodic points give an indication of where 'islands' of regular behavior will occur in the flow. The manifolds of the hyperbolic periodic point with the largest eigenvalue give a template of the striation pattern which forms in the experiments. Finally, stretching plots appear to match the experiments quite well. We have found that co-rotation of the cylinders leads to mixing over a larger region of the flow domain than the equivalent counter-rotating motion of the cylinders. Driving the cylinders with different waveforms appears to produce little or no difference in the mixing. The Melnikov method has been adapted to adjust the waveforms such that the resultant mixing is in even closer agreement. In addition, we have determined that the points which stretch the most start on the stable manifold of a hyperbolic periodic point and end up on the unstable manifold. This results in the stretching plots assuming the shape of the manifolds and consequently matching the striation patterns of the experiments. Finally, we have determined that the methods of analysis presented here can be applied to flows where only a discretized representation of the velocity field exists. This means that our methods of analysis will be effective even when the flow field must be determined numerically.
| Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:dissertations-8072 |
| Date | 01 January 1991 |
| Creators | Swanson, Paul David |
| Publisher | ScholarWorks@UMass Amherst |
| Source Sets | University of Massachusetts, Amherst |
| Language | English |
| Detected Language | English |
| Type | text |
| Source | Doctoral Dissertations Available from Proquest |
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