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Response of a spinning liquid column to pitch excitation

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Summary

The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (Ω>2Ω0) and hyperbolic (Ω<2Ω0) excitation frequency range.

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Abbreviations

a :

radius of liquid column

h :

length of column

I 1 :

modified Besselfunction of first kind and first order

J 1 :

Besselfunction of first kind and first order

r, ϕ,z :

cylindrical coordinates

t :

time

u, v, w :

velocity distribution in radial-, circumferential-and axial direction resp.

ϱ:

mass density of liquid

ξ:

free surface displacement

Φ:

velocity potential

θ0 :

rotational excitation angle

Ω0 :

velocity of spin

Ω:

forcing frequency

ω1n :

natural frequency

σ:

surface tension

Ψ:

acceleration potential

\(\alpha ^2 = 1 - \frac{{4\Omega _0^2 }}{{\omega ^2 }}\) :

for elliptic range ω>2Ω0

\(\beta ^2 = \frac{{4\Omega _0^2 }}{{\omega ^2 }} - 1\) :

for hyperbolic range ω>2Ω0

References

  1. Chun, C. H., Wuest, W.: Suppression of temperature oscillations of thermal Marangoni convection in a floating zone by superimposing of rotating flows. Acta Astron.9, 225–230 (1982).

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  2. Bauer, H. F.: Coupled oscillations of a solidly rotating liquid bridge. Acta Astronautica9, 547–563 (1982).

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  3. Bauer, H. F.: Response of a spinning liquid column to axial excitation. Acta Mechanica77, 153–170 (1989).

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  4. Bauer, H. F.: Natural frequencies and stability of circular cylindrical immiscible liquid systems. Appl. Micro. Gravity Tech. II,1, 27–44 (1989).

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Author notes

  1. H. F. Bauer

    Present address: Institut für Raumfahrttechnik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, D-8014, Neubiberg, Federal Republic of Germany

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    1. H. F. Bauer
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    Bauer, H.F. Response of a spinning liquid column to pitch excitation. Acta Mechanica 84, 1–12 (1990). https://doi.org/10.1007/BF01176084

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    • DOI: https://doi.org/10.1007/BF01176084

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