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摘要:本文列举了诸多工程领域中的液体共振运动现象,详细探讨了船舱中伴有剧烈流动的晃荡问题.描述了基于理论分析的非线性多模态方法,该方法便于波动稳定性分区、多分支解和物理稳定性的研究.强调了方形舱、垂向圆柱舱以及球形舱内伴有旋转和混沌(不规则波动)的三维流动的重要性.晃荡引起的砰击涉及到各种各样的内流条件,这些条件随液体深度与舱体长度之比而变化.针对棱柱状LNG舱,讨论了许多与流体力学和热力学参数、影响砰击载荷效应的水弹性以及模型实验缩尺比的物理现象.Abstract:Resonant liquid motions in various engineering fields are exemplified. Sloshing in ship tanks associated with violent flow are discussed in detail. A nonlinear analytically based multimodal method that facilitates investigations of wave regimes, multi-branched solutions and physical stability is described. The importance of 3D flow with, for instance, swirling and chaos in nearly square-base tanks as well as in vertical cylindrical and spherical tanks is emphasized. Sloshing-induced slamming involves a broad variety of inflow conditions that depend on the liquid depth-to-tank length ratio. The many physical phenomena involving fluid mechanic and thermodynamic parameters as well as hydroelasticity effecting slamming load effects and associated scaling from model to full scale for prismatic liquefied natural gas (LNG) tanks are discussed.
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Key words:
- multimodal method/
- sloshing/
- wave regimes/
- slamming/
- hydroelasticity/
- model test scaling
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Figure 1.Examples of typical periodic (steady-state) free-surface motions for shallow (a), intermediate (b), nearly critical (c), and finite (d) liquid depth conditions for forced horizontal oscillations with periodTnear the highest natural sloshing periodT1of two-dimensional flow in a rectangular tank. Shallow liquid conditions (a) are forh/l=0.125,h/l=0.125 ,T/T1=1. The forcing amplitude to tank breadth ratio is 0.1. Nearly-critical depth conditions (c) are forh/l= 0.35,T/T1= 0.787
Figure 2.Experimental and theoretical stability boundariesT,S, andPfor non-dimensional filling depthh/R0=0.6 and different longitudinal forcing amplitudesε=η1a/R0versus non-dimensional forcing frequencyσ/σ11. Empty (stable) and solid (unstable) symbols are experimental bounds taken from Sumner and Stofan (1963) . The symbols related toSare covered by a shadow area. Theoretical stability boundaries are marked by the solid linesT,S, andP(Faltinsen & Timokha, 2013)
Figure 3.Dimensionless steady-state wave elevation near the vertical wall =(fmax-fmin)/h(as proposed byChester and Bones(1968)) versus the excitation frequency. Rectangular tank with water depth-to-tank breadth ratioh/l= 0.08333 and 2D flow. Horizontal harmonic excitations. The calculated data are for fresh water with kinematic viscosity coefficientν=1.1×10−6m2⋅s−1. ◊ = experiments byChester and Bones(1968), dashed line = Boussinesq-type multimodal theory and solid line = theory byChester (1968). (a)η2a/l=0.001254, (b)η2a/l= 0.002583
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