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Magnetically Induced Rotating Rayleigh-Taylor Instability

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Published on: March 3, 2017

Macro-instability: a chaotic flow component in stirred tanks.

Pavel Hasal¹, Milan Jahoda, Ivan Fort

¹Department of Chemical Engineering, Institute of Chemical Technology, 166 28 Prague 6, Czech Republic. pavel.hasal@vscht.cz

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|August 4, 2007

Summary

This study analyzes chaotic macro-instability (MI) in stirred tanks using fluid velocity and force data. Key findings reveal how impeller speed and geometry influence MI dynamics, with distinct spatial variations observed for the maximum Lyapunov exponent.

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Area of Science:

Fluid Dynamics
Nonlinear Dynamics
Chemical Engineering

Background:

Stirred tanks are crucial in chemical processes.
Understanding flow instabilities is key to process optimization.
Chaotic dynamics in macro-instability (MI) require further investigation.

Purpose of the Study:

To investigate the chaotic features of macro-instability (MI) in stirred tank flow patterns.
To analyze the influence of operational conditions and geometry on MI dynamics.
To identify methods for locating regions with distinct MI dynamics.

Main Methods:

Spectral analysis to detect MI components.
Proper Orthogonal Decomposition (POD) to identify MI.
Reconstruction of attractors using POD eigenmodes or delay methods.
Evaluation of attractor invariants: correlation dimension and maximum Lyapunov exponent.

Main Results:

MI components were identified in fluid velocity and baffle force data.
Correlation dimension was insensitive to spatial location but influenced by impeller speed and geometry.
Maximum Lyapunov exponent showed significant spatial distribution and positive values, indicating chaotic behavior.
No significant spatial variability of the correlation dimension was observed.

Conclusions:

The correlation dimension and maximum Lyapunov exponent can characterize MI in stirred tanks.
These invariants can be used to pinpoint regions with different MI dynamics.
Impeller speed and vessel-impeller geometry are critical factors affecting MI.