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arXiv · 1701.04876

Are Continuum Predictions of Clustering Chaotic?

William D. Fullmer·Christine M. Hrenya
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Abstract

Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, $\lambda_1 \approx 1/\tau$, we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a result of the fundamental kinematic instability, but of the secondary (inherently multidimensional) instability.

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William D. Fullmer, Christine M. Hrenya. 2017-01-17. Are Continuum Predictions of Clustering Chaotic?. https://doi.org/10.1063/1.4977513

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