Steady-State Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion

Abstract

The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio ℎ > 1). This behavior type is supported by the existing experimental data. The wave elevations at the vertical wall are satisfactorily predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.

Resonant three-dimensional nonlinear sloshing in a square base basin. Part 5. Three-dimensional non-parametric tank forcing

“…The swirling wave amplitude is governed by the damped hard-spring-type response curves and, therefore, two different swirling waves may coexist in a certain frequency range where the forcing frequency is slightly larger than the lowest natural sloshing frequency. A novelty with regard to the same damped hard-spring type response curves for the orbitally excited swirling in an upright circular tank (Raynovskyy & Timokha 2018b) consists of two stable nearly standing waves occurring in a relatively narrow frequency range for the forcing frequency, which is slightly lower than the lowest natural sloshing frequency. The nearly standing waves co-exist with swirling.…”

“…The original and asymptotically equivalent solutions of the Narimanov-Moiseev-type modal equations differ only by the highest-order asymptotic components, which do not affect the waves stability. As a matter of the fact, studying the resonant steady-state sloshing due to periodic sway, surge, pitch, roll and yaw can be reduced to analysing the steady-state wave modes and their stability for tanks performing either reciprocating (a particular case; surveys are given by Royon-Lebeaud, Hopfinger & Cartellier (2007), Faltinsen, Lukovsky & Timokha (2016)) or orbital (relevant to bioreactors; see reviews by Weheliye, Yianneskis & Ducci (2013), Reclari et al (2014), Bouvard, Herreman & Moisy (2017), Raynovskyy & Timokha (2018b) and ) tank motions.…”

Nonlinear Sloshing of Liquid in a Rigid Cylindrical Container with a Rigid Annular Baffle under Lateral Excitation

“…Based on the multimodal method carried out in a recent paper [18], the nonlinear response of the liquid partially filled in a rigid cylindrical container with a rigid annular baffle and subjected to lateral excitation is investigated. According to Raynovskyy and Timokha [34], the significant damping can be caused by the vortex shedding at the sharp edges of the baffles. In the subsequent study, we will quantitatively study this damping based on experimental and numerical methods and then introduce it into the multimodal system.…”

“…Using the asymptotic modal method, Gavrilyuk et al [32,33] investigated the nonlinear resonant sloshing of liquid in a rigid circular cylindrical container with a rigid annular baffle. Raynovskyy and Timokha [34] studied the damped steady-state resonant sloshing in a circular base container by the nonlinear multimodal system, which is equipped with linear damping terms associated with the logarithmic decrements of the natural sloshing modes. It should be mentioned that the research on the multimodal system of containers equipped with baffles is insufficient.…”

Вимушені Коливання Паливних Баків При Різних Умовах Експлуатації

“…Ця функція може використовуватись для проектування резервуарів для рідини з кришкою. Використовуючи мультимодальну теорію плескання, автори у роботі [10] дослідили стаціонарну хвильову характеристику, коли частота вимушених коливань близька до найнижчої природної частоти хлюпання. Побудоване аналітичне рішення показує, що амплітудно-хвильова характеристика має поведінку жорсткої пружини, що підтверджується експериментально.…”