Sound Effect on Dynamics and Stability of Fluid Sloshing in Zero-Gravity

Lukovsky, Ivan A.; Timokha, Alexander

doi:10.1615/interjfluidmechres.v28.i1-2.30

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“…Using the non-conformal mapping technique by Lukovsky (1975) makes it possible to generalize the method for tanks with non-vertical walls. However, practical examples of the generalization are rare and almost fully represented by Lukovsky and Timokha (2002), Gavrilyuk et al (2005), Limarchenko (2007) and Faltinsen and Timokha (2013). A reason is that the multimodal method is rather sensitive to errors in satisfying the volume (mass) conservation condition, and, therefore, it is desirable to have analytically approximate natural sloshing modes which exactly satisfy the Laplace equation and the zero Neumann condition on the wetted tank walls.…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear sloshing in a truncated circular conical tank

Gavrilyuk¹,

Hermann²,

Lukovsky³

et al. 2013

Fluid Dyn. Res.

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Sloshing of an ideal incompressible liquid in a rigid truncated (tapered) conical tank is considered when the tank performs small-magnitude oscillatory motions with the forcing frequency close to the lowest natural sloshing frequency. The multimodal method, the non-conformal mapping technique and the Moiseev type asymptotics are employed to derive a finite-dimensional system of weakly nonlinear ordinary differential (modal) equations. This modal system is a generalization of that by Gavrilyuk et al 2005 Fluid Dyn. Res. 37 399-429. Using the derived modal equations, we classify the resonant steady-state wave regimes occurring due to horizontal harmonic tank excitations. The frequency ranges are detected where the 'planar' and/or 'swirling' steady-state sloshing are stable as well as a range in which all steadystate wave regimes are not stable and irregular (chaotic) liquid motions occur is established. The results on the frequency ranges are qualitatively supported by experiments by Matta E 2002 PhD Thesis Politecnico di Torino, Torino.

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