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Forschung im Ingenieurwesen

, Volume 65, Issue 7, pp 191–199 | Cite as

Axisymmetric natural damped frequencies of a viscous liquid in a circular cylindrical Container — An alternative semi-analytical solution

  • H. F. Bauer
  • W. Eidel
Originalarbeiten

Abstract

For axisymmetric liquid motion (m=0) in a circular cylindrical Container nlled with an incompressible and viscous liquid the natural damped frequencies are determined. The analysis satisfies the side wall conditions exactly while only the normal Container bottom condition could be satisfied. This restricts the Solution results to liquid height flllings h/a to larger values (h/a>1). It was found that with increase of the liquid height ratio h/a the oscillation frequency and decay magnitude are both increasing.

Keywords

Contact Line Viscous Liquid Free Liquid Surface Free Surface Condition Liquid Slosh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a

radius of container

g

gravity constant (g*=ga 3/ν 2)

h

liquid height

Jm

Bessel function of the first kind

p

pressure

r, ϕ, z

cylindricalpolar coordinates

\(s = \bar \sigma + i\bar \omega \)

complex frequency (S=sa 2/ν)

t

time

u, w

radial and axial liquid velocity

α2=ϱga2/σ

parameter (α 2=g*/σ *=Bo) Bond number

σ

liquid surface tension (σ*=σa/(ϱν 2))

Λn

roots of Eq. (18) (Λ n =λ n a)

ϱ

mass density

η

dynamic viscosity

ν=η/ϱ

kinematic viscosity

Ψ

stream function

Σ

free liquid surface displacement

τrz

shear stress

Axialsymmetrische schwingungen einer viskosen Flüssigkeit im zylindrischen Tank. — Eine alternative semi-analytische Lösung

Zusammenfassung

Es werden die axialsymmetrischen gedämpften Eigenfrequenzen einer viskosen Flüssigkeit im kreiszylindrischen Behälter bestimmt. Dabei werden die Zylinderwandbedingungen exakt erfüllt und für den Tankboden nur die Normalbedingung berücksichtigt. Da das Schwappen der Flüssigkeit im oberen Teil des Behälters stattfindet gilt die hier behandelte Lösung für größere Flüssigkeitshöhenverhältnisse h/a>1. Die numerischen Ergebnisse zeigen, daß mit wachsender Flüssigkeitshöhe die Schwappfrequenzen und die Abklingraten zunehmen.

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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • H. F. Bauer
    • 1
  • W. Eidel
    • 1
  1. 1.Institut für RaumfahrttechnikUniversität der Bundeswehr MünchenNeubibergGermany

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