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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Three-dimensional instabilities for the flow around a heaving foil.

Liping Sun1, Jian Deng1, Xueming Shao1

  • 1Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, P. R. China and Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China.

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Summary

This study reveals distinct Floquet modes in heaving airfoils, unlike pitching foils. Synchronous modes A and B dominate over quasiperiodic modes as instability parameters change.

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Area of Science:

  • Fluid dynamics
  • Aerodynamics
  • Instability analysis

Background:

  • Understanding flow instabilities is crucial for airfoil design.
  • Previous studies focused on pitching airfoils, leaving heaving airfoils less explored.

Purpose of the Study:

  • Investigate the three-dimensional instabilities of a periodically heaving airfoil.
  • Characterize the Floquet modes governing these instabilities.
  • Compare findings with existing research on pitching airfoils.

Main Methods:

  • Analysis of Floquet modes in the (Sr, A_D) phase space.
  • Systematic variation of frequency (Sr) and amplitude (A_D).
  • Examination of Reynolds number effects on stability.

Main Results:

  • Critical Floquet modes emerge sequentially as A, quasiperiodic (QP), and B with changing parameters.
  • Modes A and B are synchronous with the base flow, while QP is not.
  • Dominant modes shift from A to B as amplitude increases, with QP never becoming critical.
  • Subharmonic mode S is unstable but not physically realizable.

Conclusions:

  • Heaving airfoils exhibit unique instability characteristics compared to pitching foils.
  • The sequence and nature of Floquet modes are sensitive to frequency and amplitude.
  • Reynolds number influences stability similarly to amplitude variations.