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Response of differently axially excited spinning liquid columns

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Summary

A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (Ω>2Ω0) and hyperbolic range (Ω<2Ω0). Differences of the various cases are presented.

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Abbreviations

a :

radius of liquid bridge

h :

length of liquid bridge

I 0,I 1 :

modified Besselfunctions

J 0,J 1 :

Besselfunctions

p :

liquid pressure

r, ϕ,z :

cylindrical polar coordinates

t :

time

u, v, w :

velocity distribution in rotating liquid

\(\bar z_0 ,\bar z_1 ,\bar z_2 \) :

axial excitation amplitude

\(\alpha ^2 = 1 - \frac{{4\Omega _0^2 }}{{\Omega ^2 }} > 0\) :

elliptic case (Ω>2Ω0)

\(\beta ^2 = \frac{{4\Omega _0^2 }}{{\Omega ^2 }} - 1 > 0\) :

hyperbolic case (Ω<2Ω0)

ϱ:

liquid density

σ:

surface tension

ξ:

liquid surface displacement

ζ n :

damping factor

\(\bar \varphi \) :

phase angle

Ψ:

acceleration potential

Ω0 :

rotational speed

Ω, Ω1,Ω2 :

axial forcing frequency

ω:

natural frequency of rotating system

ω0n :

natural frequency of harmonic axial response

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Author notes

  1. H. F. Bauer

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

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    Bauer, H.F. Response of differently axially excited spinning liquid columns. Acta Mechanica 84, 155–173 (1990). https://doi.org/10.1007/BF01176094

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    • DOI: https://doi.org/10.1007/BF01176094

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