Resonant sloshing in an upright annular tank. (13th September 2016)

• Record Type: Journal Article
• Authors: Faltinsen, Odd M.; Lukovsky, Ivan A.; Timokha, Alexander N.
• Is Part Of: Journal of fluid mechanics. Volume 804(2016:Oct.)
• Page Start: 608
• Page End: 645
• Publication Date: 2016-09-13
• Subjects: waves/free-surface flows, -- wave–structure interactions; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.539
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : 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.