Resonant sloshing in an upright annular tank
| Autor: | Alexander Timokha, Odd M. Faltinsen, I. A. Lukovsky |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Physics
Slosh dynamics Mechanical Engineering Irregular waves 02 engineering and technology Forcing (mathematics) Radius Mechanics Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Nonlinear system 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials Excited state Modal theory 0103 physical sciences Excitation |
| Zdroj: | Journal of Fluid Mechanics. 804:608-645 |
| ISSN: | 1469-7645 0022-1120 |
| Popis: | Resonant sloshing in an upright annular tank is studied by using a new nonlinear modal theory, which is complete within the framework of the Narimanov–Moiseev asymptotics. The applicability is justified for a fairly deep liquid (the liquid-depth-to-outer-tank-radius ratio $1.5\lesssim h=\bar{h}/\bar{r}_{2}$) and away from the non-dimensional inner radii $r_{1}=\bar{r}_{1}/\bar{r}_{2}=0.08546$, 0.17618, 0.27826, 0.31323, 0.31855, 0.43444, 0.46015, 0.48434, 0.68655, 0.70118. The theory is used to describe steady-state (stable and unstable) resonant waves due to a harmonic excitation with the forcing frequency close to the lowest natural sloshing frequency. We show that the surge-sway-pitch-roll excitation is always of either longitudinal or elliptic type. Existing experimental results on the horizontally excited steady-state wave regimes in an upright circular tank ($r_{1}=0$) are utilised for validation. Inserting an inner pole with the radii $r_{1}\approx 0.25$ and 0.35 ($1.5\lesssim h$) causes that no stable swirling and/or irregular waves exist. The response curves for an elliptic-type excitation are examined versus the minor-axis forcing-amplitude component. Stable swirling is then expected being co- and counter-directed to the angular forcing direction. Passage to the rotary (circular) excitation keeps the co-directed swirling stable for all resonant forcing frequencies but the stable counter-directed swirling disappears. |
| Databáze: | OpenAIRE |
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