Sloshing motions in excited tanks
Sloshing motions in excited tanks
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DOI：
10.1016/j.jcp.2003.10.031
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发表时间：
2004-05
影响因子：
4.1
通讯作者：
J. Frandsen
中科院分区：
文献类型：
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作者：
J. Frandsen
基于无粘流动方程建立了一个完全非线性的有限差分模型。对水平和垂直运动的二维贮箱进行了晃荡波运动的数值实验。液体晃动引起的谐波基础激励的结果，提出了小到陡峭的非破碎波。模拟仅限于临界深度以上的单一水深，对应于罐纵横比hs/B=0.5。该数值模型适用于任何水深，但当粘性效应变得重要时，小水深除外。解决方案仅限于陡峭的非倾覆波。数值模式与二阶小扰动理论在小水平强迫幅值方面取得了较好的一致性。对于大的水平强迫，非线性效应由三阶单模态解和完全非线性数值模型捕获。该协议是在一般良好的，幅度和相位。正如预期的那样，三阶解比二阶解更精确。这对于共振、高强迫频率和模式相互作用的情况尤其如此。然而，它被发现，多峰近似形式应使用的情况下，失谐效应发生由于模式的相互作用。我们提出了一些测试情况下，失谐效应是显而易见的单主导模式和模式相互作用的情况下。此外，对于非常陡峭的波浪，就在波浪倾覆之前，以及对于大的强迫频率，振幅和相位的近似形式和数值模型之间发生的差异。研究了垂直和水平同时激励与纯水平运动和纯垂直运动的影响。结果表明，垂直激励引起的不稳定性与参数共振的组合运动的垂直运动的一组特定的频率和振幅，而水平运动与经典共振。还发现，除了纯水平激励的共振频率之外，由于储罐的组合运动而存在无限数量的附加共振频率。的非线性行为的解决方案上的波陡的依赖关系进行了讨论。发现对于本问题，当陡度达到约0.1时，非线性效应变得重要，这与Abramson的物理实验一致[Rep. SP 106，NASA，1966]。
A fully non-linear finite difference model has been developed based on inviscid flow equations. Numerical experiments of sloshing wave motion are undertaken in a 2-D tank which is moved both horizontally and vertically. Results of liquid sloshing induced by harmonic base excitations are presented for small to steep non-breaking waves. The simulations are limited to a single water depth above the critical depth corresponding to a tank aspect ratio of hs/b=0.5. The numerical model is valid for any water depth except for small depth when viscous effects would become important. Solutions are limited to steep non-overturning waves. Good agreement for small horizontal forcing amplitude is achieved between the numerical model and second order small perturbation theory. For large horizontal forcing, non-linear effects are captured by the third-order single modal solution and the fully non-linear numerical model. The agreement is in general good, both amplitude and phase. As expected, the third-order compared to the second-order solution is more accurate. This is especially true for resonance, high forcing frequency and mode interaction cases. However, it was found that multimodal approximate forms should be used for the cases in which detuning effects occur due to mode interaction. We present some test cases where detuning effects are evident both for single dominant modes and mode interaction cases. Furthermore, for very steep waves, just before the waves overturn, and for large forcing frequency, a discrepancy in amplitude and phase occurs between the approximate forms and the numerical model. The effects of the simultaneous vertical and horizontal excitations in comparison with the pure horizontal motion and pure vertical motion is examined. It is shown that vertical excitation causes the instability associated with parametric resonance of the combined motion for a certain set of frequencies and amplitudes of the vertical motion while the horizontal motion is related to classical resonance. It is also found that, in addition to the resonant frequency of the pure horizontal excitation, an infinite number of additional resonance frequencies exist due to the combined motion of the tank. The dependence of the non-linear behaviour of the solution on the wave steepness is discussed. It is found that for the present problem, non-linear effects become important when the steepness reaches about 0.1, in agreement with the physical experiments of Abramson [Rep. SP 106, NASA, 1966].