Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems

Abstract

Liquid parametric sloshing, known also as Faraday waves, has been a long standing subject of interest. The development of the theory of Faraday waves has witnessed a number of controversies regarding the analytical treatment of sloshing modal equations and modes competition. One of the significant contributions is that the energy is transferred from lower to higher harmonics and the nonlinear coupling generated static components in the temporal Fourier spectrum, leading to a contribution of a nonoscillating permanent sinusoidal deformed surface state. This article presents an overview of different problems of Faraday waves. These include the boundary value problem of liquid parametric sloshing, the influence of damping and surfactants on the stability and response of the free surface, the weakly nonlinear parametric and autoparametric sloshing dynamics, and breaking waves under high parametric excitation level. An overview of the physics of Faraday wave competition together with pattern formation under single-, two-, three-, and multifrequency parametric excitation will be presented. Significant effort was made in order to understand and predict the pattern selection using analytical and numerical tools. Mechanisms for selecting the main frequency responses that are different from the first subharmonic one were identified in the literature. Nontraditional sources of parametric excitation and Faraday waves of ferromagnetic films and ferrofluids will be briefly discussed. Under random parametric excitation and g-jitter, the behavior of Faraday waves is described in terms of stochastic stability modes and spectral density function.

Resonant sloshing in an upright annular tank

“…9) and Takahara & Kimura (2012). A recent review on sloshing with parametric (vertical) excitations is given by Ibrahim (2015).…”

Features of a generalized parametric resonance for a hyperboloidal reservoir

“…Тому необхідно володіти високодостовірною моделлю процесів у системах резервуаррідина, зручною для теоретичного аналізу та чисельної реалізації. Важливим класом задач є узагальнення класичної задачі Фарадея для резервуара із рідиною, що здійснює заданий рух у вертикальному напрямку [4][5][6]. Таке узагальнення проводиться у трьох напрямках [1]: рух системи «резервуар -рідина» здійснюється за наданням додаткових ступенів вільності, наприклад, дозволяється поступальний рух системи у горизонтальному напрямку, або кутовий рух резервуара; на відміну від класичної задачі Фарадея задача розглядається у сумісній постановці; розглядаються випадки не лише циліндричної форми резервуара, а й інші форми.…”

Modeling Transient Liquid Slosh Behavior at Variable Operating Speeds Induced by Intermittent Motions in Packaging Machines

“…Therefore, material parameters, such as viscosity and density, are considered as distributed parameters. Such a general approach leads to a system of partial differential equations [7][8][9]. This system of equations is not solvable analytically, wherefore numerical solution techniques such as the finite difference method or the finite volume method have to be applied [10][11][12][13].…”