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Hybrid Methods in Engineering

ISSN Print: 1099-2391

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v2.i4.70
22 pages

A MULTIMODAL APPROACH TO NONLINEAR SLOSHING IN A CIRCULAR CYLINDRICAL TANK

I. P. Gavrilyuk
Berufakademie Thuringen-Staatliche Studienakademie, 99817, Eisenach, Am Wartenberg 2, Germany
I. A. Lukovsky
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
A. N. Timokha
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine

ABSTRACT

The fluid sloshing in a mobile container of circular cylindrical shape is examined in the context of potential theory. No roof impact, overturning waves are assumed. Combined numerical-analytical modal modeling is applied. The natural modes are used as the basis of Fourier approximation of free surface evolution. Primary natural modes are assumed to be dominant. The modal system couples nonlinearly the generalized time-varying Fourier coefficients (modal functions). The secondary modes supplement is accounted for by this system, which makes possible the calculation of realistic fluid response and the visualization of wave patterns. The calculation of fluid sloshing is reduced to a Cauchy problem. The Bubnov-Galerkin variational procedure gives approximate values of the initial conditions for simulation of steady solutions. The theory is validated by experimental data. Modal modeling guarantees time—efficient and robust simulations. Multidimensional structure gives more realistic surface wave patterns and may thereby improve the calculation of force (moment) response. The theory breaks down as the wave amplitude response exceeds 45% of the radius.