Skip to main content
SpringerLink
Log in

Response of a spinning liquid column to axial excitation

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The response of a solidly rotating finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined in the elliptic (Ω>2Ω 0) and hyperbolic frequency range (Ω>2Ω 0).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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

\(\bar z_0 \) :

axial excitation amplitude

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

elliptic case (Ω>2Ω 0)

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

hyperbolic case (Ω>2Ω 0)

ϱ:

liquid density

σ:

surface tension

ζ:

liquid surface displacement

Ψ:

acceleration potential

Ω 0 :

rotational speed

Ω:

axial forcing frequency

ω:

natural frequency of rotating system

ω 02n −1:

natural frequency of harmonic axial response

References

  1. Reyleigh, J.: On the capillary phenomenon of jets. Proc. Roy. Soc. London29, 71–97 (1879).

    Google Scholar 

  2. Rayleigh, J.: Theory of sound. New York: Dover 1945.

    Google Scholar 

  3. Lamb, H.: Hydrodynamics. Cambridge: University Press 1932.

    Google Scholar 

  4. Bauer, H. F.: Natural damped frequencies of an infinitely long column of immiscible viscous liquids. Forsch. Ing. Wes.49, 117–126 (1983).

    Google Scholar 

  5. Bauer, H. F.: Natural damped frequencies of an infinitely long column of immiscible viscous liquids. ZAMM64, 475–490 (1984).

    Google Scholar 

  6. Bauer, H. F.: Free surface- and interface oscillations of an infinitely long visco-elastic liquid column. Acta Astronautica13, 9–22 (1986).

    Google Scholar 

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

    Google Scholar 

  8. Bauer, H. F.: Axial response, transient- and pulse behavior of a cylindrical liquid column in zero gravity. Forschungsbericht Universität der Bundeswehr München, UniBw-WE-9-FB-9-1988.

  9. Bauer, H. F.: Response of a spinning liquid column to axial excitation. Forschungsbericht Universität der Bundeswehr München, UniBw-WE-9-FB-10-1988.

Download references

Author information

Authors and Affiliations

  1. Institut für Raumfahrttechnik, Universität der Bundeswehr, Werner-Heisenberg-Weg 39, D-8014, Neubiberg, Germany

    H. F. Bauer

Authors
  1. H. F. Bauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 8 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bauer, H.F. Response of a spinning liquid column to axial excitation. Acta Mechanica 77, 153–170 (1989). https://doi.org/10.1007/BF01178319

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01178319

Keywords

Search

Navigation