Nonlinear Sloshing Integrated Aeroelastic Analyses of a Research Wing Prototype

Two-dimensional nonlinear sloshing of an incompressible fluid with irrotational flow in a rectangular tank is analysed by a modal theory. Infinite tank roof height and no overturning waves are assumed. The modal theory is based on an infinite-dimensional system of nonlinear ordinary differential equations coupling generalized coordinates of the free surface and fluid motion associated with the amplitude response of natural modes. This modal system is asymptotically reduced to an infinite-dimensional system of ordinary differential equations with fifth-order polynomial nonlinearity by assuming sufficiently small fluid motion relative to fluid depth and tank breadth. When introducing inter-modal ordering, the system can be detuned and truncated to describe resonant sloshing in different domains of the excitation period. Resonant sloshing due to surge and pitch sinusoidal excitation of the primary mode is considered. By assuming that each mode has only one main harmonic an adaptive procedure is proposed to describe direct and secondary resonant responses when Moiseyev-like relations do not agree with experiments, i.e. when the excitation amplitude is not very small, and the fluid depth is close to the critical depth or small. Adaptive procedures have been established for a wide range of excitation periods as long as the mean fluid depth h is larger than 0.24 times the tank breadth l. Steady-state results for wave elevation, horizontal force and pitch moment are experimentally validated except when heavy roof impact occurs. The analysis of small depth requires that many modes have primary order and that each mode may have more than one main harmonic. This is illustrated by an example for h/l = 0.173, where the previous model by Faltinsen et al. (2000) failed. The new model agrees well with experiments.

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Investigation of nonlinear sloshing effects in seismically excited tanks

Soil Dynamics and Earthquake Engineering ◽

10.1016/j.soildyn.2012.08.001 ◽

2012 ◽

Vol 43 ◽

pp. 355-365 ◽

Cited By ~ 32

Author(s):

Mohammad Ali Goudarzi ◽

Saeed Reza Sabbagh-Yazdi

Keyword(s):

Nonlinear Sloshing

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Study on the Predictive Evaluation Method of Load Acting on the Roof and Internal Components of Cylindrical Tanks by Nonlinear Sloshing

Volume 9: Seismic Engineering ◽

10.1115/pvp2020-21343 ◽

2020 ◽

Author(s):

Hideyuki Morita ◽

Tomoshige Takata ◽

Hideki Madokoro ◽

Hiromi Sago ◽

Shinobu Yokoi ◽

...

Keyword(s):

Wave Height ◽

Seismic Isolation ◽

Liquid Surface ◽

Impact Load ◽

Response Spectrum ◽

Free Liquid Surface ◽

Past Study ◽

Long Period ◽

Nonlinear Sloshing ◽

Cylindrical Tanks

Abstract When cylindrical tanks installed in the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the free liquid surface inside the tank called sloshing may occur. If high-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage of the tank roof or outflow of internal liquid of the Tank. Therefore, it is important to predict the wave height of sloshing generated by earthquake motions. Sloshing is a type of vibration of free liquid surface, and if the sloshing wave height is small, it can be approximated with a linear vibration model. In this case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under earthquake motions. However, if the sloshing wave height increases, the sloshing becomes nonlinear, and necessary to evaluate the wave height using other methods such as numerical analysis. Design earthquake magnitude levels in Japan tend to increase in recent years, long-period components of earthquake wave which act on the sloshing wave height also increase instead of introducing seismic isolation mechanisms. To evaluate load acting on the internal components of cylindrical tanks by nonlinear sloshing, there are few applications which quantitatively evaluated the crest impact load of nonlinear sloshing. In order to evaluate the load acting on the internal components of cylindrical tanks, the range of applicability of the fluid flow analysis method which validated the analysis accuracy of impact load acting on the roof in a simple cylindrical tank in the past study (PVP2019-93442) is extended to cylindrical tanks with internal components.

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