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(searched for: doi:10.1299/kikai1938.44.3024)
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Mohammed F. Daqaq, Yawen Xu, Walter Lacarbonara
Published: 22 December 2016
Journal of Applied Mechanics, Volume 84; https://doi.org/10.1115/1.4035363

Abstract:
This paper investigates the influence exerted by small surface tension on the nonlinear normal sloshing modes of a two-dimensional irrotational, incompressible fluid in a rectangular container. To this end, the influence of surface tension on the modal frequencies is investigated by assuming pure slipping at the contact line and a 90 deg contact angle between the fluid surface and the walls. The regions of possible nonlinear internal resonances up to the fifth mode are highlighted. Away from the highlighted regions, the influence of surface tension on the effective nonlinearity of the lowest four modes is studied and used to shed light onto its effect on the softening/hardening behavior of the uncoupled nonlinear modes. Subsequently, the response of the sloshing waves near two-to-one internal resonances is studied. It is shown that, in the vicinity of such internal resonance, the steady-state sloshing response can either contain a contribution from the two interacting modes (coupled-mode response) or only the high-frequency mode (high-frequency uncoupled mode response). The regions where the coupled mode uniquely exists are shown to depend on the surface tension. Moreover, it is demonstrated that such regions may be underestimated considerably when neglecting the influence of the cubic nonlinearities.
, Takashi Nagaya
Earthquake Engineering & Structural Dynamics, Volume 42, pp 973-991; https://doi.org/10.1002/eqe.2254

Abstract:
A hybrid analytical and FEM is proposed to investigate the nonlinear sloshing in a floating-roofed oil storage tank under long-period seismic ground motion. The tank is composed of a rigid cylindrical wall and a flat bottom, whereas the floating roof is treated as an elastic plate undergoing large deflection. The contained liquid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The method of analysis is based on representation of the liquid motion by superposing the analytical modes that satisfy the Laplace equation and the rigid wall and bottom boundary conditions. The FEM is then applied to solve the remaining kinematic and dynamic boundary conditions at the moving liquid surface coupled with the nonlinear equation of motion of the floating roof. This requires only the discretization of the liquid surface and the floating roof into finite elements, thus leading to a computationally efficient and accurate method compared with full numerical analysis. As numerical examples to illustrate the applicability of the proposed method, two oil storage tanks with single-deck type floating roofs damaged during the 2003 Tokachioki earthquake are studied. It is shown that the nonlinear oscillation modes with the circumferential wave numbers 0, 2 and 3 caused by the finite liquid surface elevation as well as the membrane action due to large deflection of the deck produce excessively large stresses in the pontoon, which may cause the catastrophic failure of pontoon followed by the submergence of the roof. Copyright © 2012 John Wiley & Sons, Ltd.
Modeling Multiphase Materials Processes pp 169-213; https://doi.org/10.1007/978-1-4419-7479-2_5

Abstract:
A liquid in a rigid vessel subjected to external forced excitation becomes unstable under certain conditions due to strong nonlinear effects [1–12]. A variety of modes of liquid surface oscillations occur such as rotary sloshing or swirl. Such oscillations exert significant influence on the safety of cylindrical tanks preserving petroleum, tankers carrying petroleum, rocket boosters, and liquid containers in many chemical and mechanical plants. When the amplitudes of the oscillations are sufficiently large, the vessels are sometimes destroyed or ruptured, resulting in huge economic losses. A number of theoretical and experimental investigations have been done to understand the oscillation modes of liquids in circular cylindrical tanks [6, 10], spherical tanks [7, 10], sector-compartmented circular cylindrical tanks [3, 8], and long rectangular tanks [12]. Some aspects of the rotary sloshing or swirl are briefly reviewed in this section.
Moriyoshi Shitara, Manabu Iguchi, Keiji Takano, Taku Tamamori, Hidehiro Shitara, Toshihiko Maruyama
Journal of the Japan Institute of Metals and Materials, Volume 68, pp 927-931; https://doi.org/10.2320/jinstmet.68.927

Manabu Iguchi, Tsuneo Kondoh, Keiji Nakajima
Metallurgical and Materials Transactions B, Volume 28, pp 605-612; https://doi.org/10.1007/s11663-997-0032-4

Abstract:
The establishment time of gas-liquid two-phase flows in a cylindrical bath agitated by bottom gas injection through a central single-hole bottom nozzle was investigated. Because the turbulence intensity in the bath was comparable to or larger than the unity, the conventional definition of the flow establishment time based on the history of mean velocity was not suitable for the present case. In fact, it was difficult to determine the flow establishment time based on the well-known 90 or 99 pct criterion for the mean velocity. Accordingly, two methods of determining the flow establishment time by focusing on the turbulence components instead of the mean velocity components were proposed. Velocity measurements were made with a two-channel laser Doppler velocimeter. The flow establishment time was correlated as a function of gas flow rate. Close agreement was obtained by the two methods.
Manabu Iguchi, Tsuneo Kondoh, Tomomasa Uemura, Fujio Yamamoto, Zen-Ichiro Morita
Published: 1 February 1994
Experiments in Fluids, Volume 16, pp 255-262; https://doi.org/10.1007/bf00206545

Abstract:
Gas injection into a cylindrical bath through a centric bottom nozzle causes a swirl motion like rotary sloshing. Conditions indicating the initiation and cessation of the swirl motion have been made clear by many researchers. So far, the effect of the swirl motion on transport phenomena in the bath is not clear yet. The present study was made to clarify the bubble characteristics (void fraction, bubble frequency) and liquid flow characteristics (mean velocity, turbulence intensity, Reynolds shear stress) during swirl motion of bubbling jet. These two characteristics were investigated using an electro-resistivity probe and a two-dimensional LDV, respectively.
K. Komatsu
International Journal of Non-Linear Mechanics, Volume 22, pp 193-207; https://doi.org/10.1016/0020-7462(87)90002-3

Abstract:
A method is newly proposed for calculating the non-linear dynamic behavior of liquid in tanks with arbitrary geometries. The formulation uses the orthogonality of the linear mode shapes and the numerical perturbation technique. The problem is reduced to the non-linear coupled ordinary differential equations describing the timewise trend. Numerical examples carried out on the sloshing in rectangular and axisymmetric tanks demonstrate the versatility of the present method.
M. Utsumi, K. Kimura, M. Sakata
Published: 8 September 1984
Journal of Sound and Vibration, Volume 96, pp 83-99; https://doi.org/10.1016/0022-460x(84)90596-0

Abstract:
An investigation of the non-stationary hydroelastically coupled motion of a rectangular container with elastic walls, partially filled with liquid, in response to a random excitation, is described. Calculations are presented of the mean and standard deviation responses to an amplitude modulated non-white random excitation of the displacement of the liquid surface and the deformation of the walls. Consideration of non-linearity is found to be indispensable in the case of earthquake excitation, with a low dominant frequency, since the non-linear analysis leads to positive values of the mean responses of the liquid surface and wall displacement, while the linearized theory predicts zero mean response.
M. Sakata, K. Kimura, M. Utsumi
Published: 8 June 1984
Journal of Sound and Vibration, Volume 94, pp 351-363; https://doi.org/10.1016/s0022-460x(84)80016-4

Abstract:
The non-stationary response of non-linear liquid motion in a cylindrical tank subjected to lateral earthquake excitation is investigated by modeling the earthquake excitation as an amplitude modulated non-white random process having a dominat frequency. The non-stationary standard deviation and mean responses of the liquid surface displacement are calculated and it is shown that the linear liquid motion theory is not necessarly sufficient to evaluate the safety of tanks, since the non-linear analysis leads to a positive value of the mean response for the liquid surface displacement at the tank wall, while the linear theory predicts zero mean response.
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