Numerical simulation analysis of liquid sloshing in tank under random excitation
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摘要:
目的 研究随机激励条件下矩形液舱内的瞬态效应、不同谱峰频率与有义激励振幅对液舱晃荡的影响。 方法 采用计算流体力学（CFD）方法建立数值模型，通过与线性势流解析解和实验数据进行对比，验证所提数值模型的可靠性。 结果 结果显示，随机激励瞬态效应对液舱晃荡自由水面变化有显著影响，通过施加缓冲函数可以较快地获取稳定结果；当激励谱谱峰频率接近液舱晃荡固有频率时，液舱晃荡波高响应谱的能量主要集中在液舱的固有频率处，而当激励谱谱峰频率远离液舱晃荡固有频率时，液舱晃荡波高响应谱的能量主要集中在谱峰频率附近；随着激励谱有义振幅的增大，液舱晃荡响应相对于线性波（偏离度为0）其振幅偏离度增大，液舱的非线性显著增强。 结论 对于随机激励的模拟，尤其是激励频率远离固有频率时，对激励历时线进行缓冲函数处理非常有必要；当谱峰频率远离一阶固有频率向更高频移动，在接近第i阶固有频率时，该频率处的峰值将占主导。 Abstract:Objectives This paper studies the transient effects, different frequencies of spectral peaks and meaningful excitation amplitudes on liquid sloshing. Methods A numerical model is established using the computational fluid dynamics (CFD) method, and the reliability of the numerical model is validated through comparison with the analytical solution of linear potential flow and experimental data. Results The transient effects of random excitation have a significant influence on the fluctuation of the free water surface of liquid sloshing in the tank. By applying the buffer function, stable results can be obtained quickly. When the peak frequency of the excitation spectrum is close to the natural frequency of the tank, the energy of the wave-height response spectrum of the liquid sloshing in the tank is mainly concentrated at the natural frequency of the tank. When the peak frequency of the excitation spectrum is far from the natural frequency of the tank, the energy of the wave-height response spectrum is concentrated near the peak frequency. With the increase of the meaningful amplitude of the excitation spectrum, the amplitude deviation of the liquid sloshing response relative to the linear wave (the deviation degree is zero) increases, and the nonlinearity of the tank increases significantly. Conclusions For the random excitation simulation, especially when the excitation frequency is far from the natural frequency, it is necessary to buffer the excitation duration. It is found that when the peak frequency of the excitation spectrum moves away from the first natural frequency to higher frequencies, the energy is dominant at the i-th order of the natural frequency when the peak frequency is close to it. -
Key words:
- liquid sloshing /
- random excitation /
- transient effect /
- numerical simulation
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图 2 工况1和工况2下右舱壁波高历程线比较图
Figure 2. Comparison of the right bulkhead wave height at Case 1 and Case 2
图 3 工况3和工况4下右舱壁波高历程线比较图
Figure 3. Comparison of the right bulkhead wave height at Case 3 and Case 4
图 5 工况1下右舱壁波高在100~500 s时间段的FFT谱分析
Figure 5. Fast Fourier transform power spectrum analysis of right bulkhead wave height during 100~500 s at Case 1
图 7 工况2右舱壁波高100~500 s时间段FFT谱分析
Figure 7. Power spectrum analysis of right bulkhead wave height during 100~500 s at Case 2
图 9 右舱壁波高概率密度分布图（
${\omega }_{\text{p}}=0.65{\omega }_{0}\text{ }，\text{ }{H}_{\rm{s}}=0.01d$ ）Figure 9. Probability density distribution of right bulkhead wave height (
${\omega }_{\text{p}}=0.65{\omega }_{0}\text{ }，\text{ }{H}_{\rm{s}}=0.01d$ )
图 10 右舱壁波高概率密度分布图（
${\omega }_{\text{p}}={\omega }_{0}\text{ }，\text{ }{H}_{\rm{s}}=0.01d$ ）Figure 10. Probability density distribution of right bulkhead wave height (
${\omega }_{\text{p}}={\omega }_{0}\text{ }，\text{ }{H}_{\rm{s}}=0.01d$ )
图 11 右舱壁波高概率密度分布图（
${\omega }_{\text{p}}=1.5{\omega }_{0}\text{ }，\text{ }{H}_{\rm{s}}=0.01d$ ）Figure 11. Probability density distribution of right bulkhead wave height (
${\omega }_{\text{p}}=1.5{\omega }_{0}\text{ }，\text{ }{H}_{\rm{s}}=0.01d$ )
图 13 右舱壁波高能量谱（
${\omega _{\text{p}}} \leqslant {\omega _0}{\text{ }},{\text{ }}{H_{\rm{s}}} = 0.01d$ ）Figure 13. Power spectrum of right bulkhead wave height (
${\omega _{\text{p}}} \leqslant {\omega _0}{\text{ }},{\text{ }}{H_{\rm{s}}} = 0.01d$ )
图 14 右舱壁波高能量谱（
${\omega _{\text{p}}} > {\omega _0}{\text{ }},{\text{ }}{H_{\rm{s}}} = 0.01d$ ）Figure 14. Power spectrum of right bulkhead wave height (
${\omega _{\text{p}}} > {\omega _0}{\text{ }},{\text{ }}{H_{\rm{s}}} = 0.01d$ )
图 16 右舱壁波高概率密度分布图（
${H_{\rm{s}}} = 0.01d$ ）Figure 16. Probability density distribution of right bulkhead wave height (
${H_{\rm{s}}} = 0.01d$ )表 1 振幅周期统计分析
Table 1. Statistical analysis of amplitude and period
${\omega _{\rm{p}}}$ 时间段 100~500 s 500~900 s 900~1 300 s Aave/m 0.65${\omega _0}$ 0.024 0.027 0.026 ${\omega _0}$ 0.042 0.039 0.040 1.5${\omega _0}$ 0.026 0.025 0.028 T/s 0.65${\omega _0}$ 0.928 0.817 0.820 ${\omega _0}$ 1.049 0.995 1.032 1.5${\omega _0}$ 0.743 0.785 0.783 
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表 2 标准差统计分析
Table 2. Statistical analysis of standard deviation
激励幅值Hs 右舱壁波高标准差 水平力标准差 0.002d 0.009 75 34.81 0.006d 0.031 02 96.22 0.010d 0.023 81 142.99
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