Experimental study on mooring tension of a moored rectangular cylinder under freak wave
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摘要: 基于物理模型试验，探究畸形波和不规则波作用下浮体系泊张力差异问题。讨论相对波高、相对周期和畸形波参数α1对系泊张力的影响。结果显示：畸形波参数α1和浮体系泊张力显著相关。在α1=2.0～2.83范围内，畸形波作用下迎浪侧系泊张力最大值可达不规则波作用的1.9倍。在相对波高Hs/d=0.032～0.097范围内，畸形波作用下迎浪侧系泊张力最大值显著大于不规则波的作用结果，但畸形波和不规则波对应的1/3值及平均值几乎一致。就相对周期影响而言，迎浪侧系泊张力最大差别出现在谱峰周期Tp<T0p范围内。频域方面采用小波分析方法讨论畸形波和不规则波作用下浮体系泊张力时频谱特征，两种波浪作用下系泊张力时频特征有显著差别。Abstract: Based on extensive experiments on the mooring tension of a rectangular cylinder, the present investigation compares the mooring tension of a floating rectangular cylinder under freak and random waves and quantifies the difference through experimental measurements. The effects of the relative wave height, relative period and freak wave parameter α1 on the mooring tension are investigated. The results show that, the freak wave parameter α1 has significant effect on the mooring tension of the floater. With α1=2.0～2.83, the maximum mooring tension under freak wave were 1.9 times larger than that under random wave. With Hs/d=0.032～0.097, the maximum mooring tension under freak wave are significantly larger than those under irregular waves, but the 1/3 large value and average value under freak and irregular waves are almost the same. For the effect of the relative period, the critical variation of mooring tension occur at period within Tp<T0p. The time-frequency spectra of the mooring tension under freak and random waves are calculated by wavelet analysis to investigate the time-frequency structure characteristics and variation. The time-frequency characteristics of mooring tension are significantly different from those of random wave.
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Key words:
- freak wave /
- moored rectangular cylinder /
- mooring tension /
- wavelet analysis
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图 2 模型系泊方式及在水槽中的布置
a. 模型布置实况；b. 平面布置图；c. 立面布置图
Fig. 2 Mooring pattern and layout of the model in the wave flume
a. Model placement; b. floor plan; c. elevation plan
图 3 浮体运动及迎浪侧系泊张力幅值响应算子试验结果
Fig. 3 Response amplitude operators of the motion responses and mooring tension
图 4 缆绳系泊张力历时曲线（Hs=8.0 cm，Tp=1.14 s）
Fig. 4 Time history of mooring tension of the floater (Hs=8 cm, Tp=1.14 s)
图 5 畸形波和不规则波作用下缆绳迎浪侧系泊张力随相对波高变化比较（Hs/d=0.032～0.097，Tp=1.4 s）
Fig. 5 Comparison of the mooring tension varying with the relative wave height under the freak and random waves (Hs/d=0.032～0.097, Tp=1.4 s)
图 6 系泊张力统计特征值比值随相对波高变化（Hs/d=0.032～0.097，Tp=1.4 s）
Fmax(f)/Fmax(i)、F1/10(f)/F1/10(i)、F1/3(f)/F1/3(i)和Faverage(f)/Faverage(i)分别表示畸形波与不规则波作用时，浮体迎浪侧系泊张力最大值、1/10大值、1/3大值及平均值之比
Fig. 6 The variation of statistical characteristics of mooring tension versus the relative wave height (Hs/d=0.032～0.097, Tp=1.4 s)
Fmax(f)/Fmax(i), F1/10(f)/F1/10(i), F1/3(f)/F1/3(i), and Faverage(f)/Faverage(i) are the ratio of the maximum value, 1/10 value, 1/3 value and the average value of the mooring tension under freak and random waves
图 7 畸形波和不规则波作用下缆绳系泊张力随相对周期变化（Hs=8 cm，Tp/T0p=0.57～1.55）
Fig. 7 Comparison of the mooring tension varying with the relative period under the freak and random waves (Hs=8 cm, Tp/T0p=0.57～1.55)
图 8 迎浪侧系泊张力最大值比值随相对周期变化（Hs=8 cm，Tp/T0p=0.57～1.55）
Ff /Fi表示畸形波与不规则波作用时，浮体迎浪侧系泊张力最大值比值
Fig. 8 The variation of statistical characteristics of mooring tension versus the relative period (Hs=8 cm, Tp/T0p=0.57～1.55)
Ff /Fi represents the ratio of the maximum mooring tension on the windward side of the floating body under the freak and random waves
图 9 畸形波和不规则波作用下系泊张力随畸形波参数α1变化（Hs=8 cm，Tp=1.6 s）
Fig. 9 Comparison of the mooring tension varying with α1 under freak and random waves (Hs=8 cm, Tp=1.6 s)
图 10 不同波高和周期条件畸形波和不规则波作用下缆绳系泊张力时频谱对比
Fig. 10 Time-frequency spectra of mooring tension under the freak and random waves of different conditions
a−d. Hs=8.0 cm, Tp=1.14 s; e−h. Hs=13.6 cm, Tp=1.4 s; i−l. Hs=8.0 cm, Tp=1.4 s
图 11 不同波高和周期条件下畸形波和不规则波作用下系泊张力“广义能量谱”E(t)对比
a, b. Hs=8.0 cm, Tp=1.14 s; c, d. Hs=13.6 cm, Tp=1.4 s; e, f. Hs=8.0 cm, Tp=1.4
Fig. 11 Generalized energy spectrum of mooring tension under the freak and random waves of different conditions
表 1 浮体模型几何尺寸及水动力参数
Tab. 1 Mechanical parameters of the rectangular cylinder
参数 原型值 模型值 边长/m 17.5 0.50 高度/m 22 0.62 边角圆弧半径/m 2.3 0.066 吃水深度/m 12.0 0.34 重量/t 3130 0.073 重心高度/m 7.0 0.20 浮心高度/m 6.0 0.17 横/纵稳心半径/m 2.15 0.061 3 横/纵稳性高度/m 1.8 0.051 3 纵荡自振周期T0s/s 59.0 10.0 垂荡自振周期T0h/s 8.3 1.4 纵摇自振周期T0p/s 11.8 2.0 
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表 2 试验组别及相关参数
Tab. 2 Summary of test groups and correlation parameters
试验序列 畸形波及不规则波 畸形波 备注 有效波高/cm 谱峰周期/s 相对波高 相对周期 畸形波参数α1 畸形波参数α2-α4 Tp/T0s Tp/T0h Tp/T0p I：有效波高变化序列，谱峰周期固定 4.54 1.40～1.45 0.032 0.14～0.15 1.00～1.04 0.70～0.73 2.10<α1<2.20 1.72<α2<2.10
1.55<α3<2.10
0.53<α4<0.62考察波高影响 6.51 0.047 8.52 0.061 10.54 0.075 11.80 0.084 13.62 0.097 II：谱峰周期变化序列, 有效波高固定 7.86～8.15 1.14 0.056～0.058 0.11 0.81 0.57 2.00<α1<2.20 1.40<α2<2.14
1.40<α3<2.37
0.51<α4<0.66考察周期影响 1.26 0.13 0.90 0.63 1.56 0.16 1.11 0.78 1.83 0.18 1.31 0.92 2.01 0.20 1.44 1.01 2.16 0.22 1.54 1.08 2.87 0.29 2.05 1.44 3.10 0.31 2.21 1.55 III：畸形波参数α1变化，谱峰周期和
有效波高固定7.77～8.11 1.56～1.60 0.056～0.058 0.16～0.16 1.11～1.14 0.78～0.80 1.91 考察畸形波参数αn的影响 2.07 1.30<α2<1.52 2.32 1.50<α3<1.94 2.60 0.51<α4<0.56 2.83 试验序列 规则波 波高/cm 周期/s 相对波高 相对周期 备注 Tp/T0s Tp/T0h Tp/T0p IV：附加规则波
试验序列10.00 1.00 0.07 0.10 0.71 0.50 获取浮式结构物幅值响应算子RAO以及相关的相位响应 1.20 0.12 0.86 0.60 1.40 0.14 1.00 0.70 1.60 0.16 1.14 0.80 1.80 0.18 1.29 0.90 2.00 0.20 1.43 1.00 2.20 0.22 1.57 1.10 2.40 0.24 1.71 1.20 2.60 0.26 1.86 1.30 2.80 0.28 2.00 1.40 3.00 0.30 2.14 1.50 3.20 0.32 2.29 1.60 3.40 0.34 2.43 1.70
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