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Are continuum predictions of clustering chaotic?
William D Fullmer1, Christine M Hrenya1
1Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, USA.
Chaos (Woodbury, N.Y.)
|April 3, 2017
Summary
Gas-solid multiphase flows exhibit clustering instability. Continuum models predict chaotic behavior, not simple periodicity, indicating sensitive dependence on initial conditions and a positive largest Lyapunov exponent.
Area of Science:
- Fluid Dynamics
- Computational Physics
- Chemical Engineering
Background:
- Gas-solid multiphase flows frequently exhibit clustering, an instability leading to complex spatiotemporal patterns.
- Two-fluid models are widely used to simulate these flows, but the nature of the predicted patterns (truly aperiodic vs. complex periodic) remains unclear.
Purpose of the Study:
- To determine if continuum model predictions of clustering instability in gas-solid flows are chaotic.
- To investigate the dimensional dependence of this chaotic behavior.
Main Methods:
- Analysis of sensitive dependence on initial conditions.
- Calculation of the largest Lyapunov exponent (λ 1 ) for the system.
- Examination of the behavior across different system dimensions.
Main Results:
- The study provides evidence that continuum predictions of clustering instability exhibit sensitive dependence on initial conditions.
- A positive largest Lyapunov exponent (λ 1 ≈1/τ) was calculated, indicating chaotic dynamics.
- The chaotic behavior was found to be dimensionally dependent.
Conclusions:
- Continuum model simulations of gas-solid flow clustering display chaotic dynamics, rather than simple periodicity.
- This chaotic behavior is not solely due to the fundamental kinematic instability but requires a secondary, multidimensional instability.
- The dimensional dependence unifies previous simulation results and clarifies the nature of predicted clustering patterns.
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