The effect of finite Reynolds numbers on chaotic advection is investigated for two
dimensional lid-driven cavity flows that exhibit topological chaos in the creeping flow
regime. The emphasis in this endeavor is to study how the inertial effects present
due to small, but non-zero, Reynolds number influence the efficacy of mixing. A
spectral method code based on the Fourier-Chebyshev method for two-dimensional
flows is developed to solve the Navier-Stokes and species transport equations. The
high sensitivity to initial conditions and the exponentional growth of errors in chaotic
flows necessitate an accurate solution of the flow variables, which is provided by the
exponentially convergent spectral methods. Using the spectral coefficients of the basis
functions as solved through the conservation equations, exponentially accurate values
of velocity everywhere in the flow domain are obtained as required for the Lagrangian
particle tracking. Techniques such as Poincare maps, the stirring index based on the
box counting method, and the tracking of passive scalars in the flow are used to
analyze the topological chaos and quantify the mixing efficiency.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2009-12-7609 |
| Date | 2009 December 1900 |
| Creators | Rao, Pradeep C. |
| Contributors | Duggleby, Andrew T. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | application/pdf |
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