Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth
Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth
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DOI：
10.1017/jfm.2016.872
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发表时间：
2017-01
影响因子：
3.7
通讯作者：
H. Santo;P. Taylor;E. C. Moreno;P. Stansby;R. Taylor;Liang Sun;Jun Zang
中科院分区：
文献类型：
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作者：
H. Santo;P. Taylor;E. C. Moreno;P. Stansby;R. Taylor;Liang Sun;Jun Zang
本文对多体波能转换器在恶劣海况下的极限响应进行了线性和非线性分析。被称为M4的WEC由三个圆柱形浮子组成，其直径和吃水深度从船头到船尾增加，较大的中部和船尾浮子具有圆形底座，因此整个系统的阻力效应可以忽略不计。船头和中间浮子通过梁刚性连接，船尾浮子通过梁连接到中间浮子上方的铰链，其中旋转相对运动将被阻尼以在操作条件下吸收动力。一系列代表极端波浪的集中波群在无铰链阻尼的比例模型上进行了测试，也代表了具有多模式强迫的互连圆柱形浮子的更一般的系统。重要的是，分析揭示了一个主要的线性响应结构的铰链角和弱非线性响应的梁弯矩，而由于漂移力的影响，预计主要是二阶，没有考虑。在主波群驱动下的激振阶段，模型还存在复杂而剧烈的自由面效应，这些自由面效应通常会降低模型的整体运动响应。一旦主群离开，自由振动阶段的衰减响应以非常接近简单线性辐射阻尼预测的速率衰减。两种类型的非线性谐波运动证明。在自由振动阶段，只有两倍和三倍频率的斯托克斯谐波的线性运动，捕获使用倍频和三倍频模型。相反，在激励阶段，这些谐波表现出与非线性流体负载相关的复杂得多的行为。虽然在系统响应中可以看到束缚谐波，但在中心浮子暂时浸没（“浸泡”）之前，整体响应是非常线性的。这为大于${\sim}30^{\circ }$的角振幅提供了强大的稳定效果，只要淹没继续，就可以将其视为驱动波部分的暂时损失。与实验和数值推导的响应振幅算子（RAO），我们进行了统计分析的极端响应的铰链角的基础上波数据在奥克尼，众所周知的严重的波浪气候，使用NORA 10波后报。对于谱峰波周期长于RAO峰周期的风暴，响应由海况的陡度而不是波高控制。因此，系统在最极端海况下的响应非常相似，为最可能的最大响应提供了上限，在定向传播波中，该上限显著降低。这里提出的方法是相关的其他单和多体系统，包括WEC。我们还展示了一个一般的和潜在的重要的互惠结果在随机海洋中的线性体运动：平均波的历史给出了一个极端的系统响应和平均响应历史给出了一个极端的波匹配的时间，与时间反转的信号之一。这种关系将提供一个有效的和强大的方式来定义一个“设计师波”，实验测试和计算密集型计算流体动力学（CFD），为广泛的波结构相互作用的问题。
This paper presents both linear and nonlinear analyses of extreme responses for a multi-body wave energy converter (WEC) in severe sea states. The WEC known as M4 consists of three cylindrical floats with diameters and draft which increase from bow to stern with the larger mid and stern floats having rounded bases so that the overall system has negligible drag effects. The bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the rotational relative motion would be damped to absorb power in operational conditions. A range of focussed wave groups representing extreme waves were tested on a scale model without hinge damping, also representing a more general system of interconnected cylindrical floats with multi-mode forcing. Importantly, the analysis reveals a predominantly linear response structure in hinge angle and weakly nonlinear response for the beam bending moment, while effects due to drift forces, expected to be predominantly second order, are not accounted for. There are also complex and violent free-surface effects on the model during the excitation period driven by the main wave group, which generally reduce the overall motion response. Once the main group has moved away, the decaying response in the free-vibration phase decays at a rate very close to that predicted by simple linear radiation damping. Two types of nonlinear harmonic motion are demonstrated. During the free-vibration phase, there are only double and triple frequency Stokes harmonics of the linear motion, captured using a frequency doubling and tripling model. In contrast, during the excitation phase, these harmonics show much more complex behaviour associated with nonlinear fluid loading. Although bound harmonics are visible in the system response, the overall response is remarkably linear until temporary submergence of the central float (‘dunking’) occurs. This provides a strong stabilising effect for angular amplitudes greater than ${\sim}30^{\circ }$ and can be treated as a temporary loss of part of the driving wave as long as submergence continues. With an experimentally and numerically derived response amplitude operator (RAO), we perform a statistical analysis of extreme response for the hinge angle based on wave data at Orkney, well known for its severe wave climate, using the NORA10 wave hindcast. For storms with spectral peak wave periods longer than the RAO peak period, the response is controlled by the steepness of the sea state rather than the wave height. Thus, the system responds very similarly under the most extreme sea states, providing an upper bound for the most probable maximum response, which is reduced significantly in directionally spread waves. The methodology presented here is relevant to other single and multi-body systems including WECs. We also demonstrate a general and potentially important reciprocity result for linear body motion in random seas: the averaged wave history given an extreme system response and the average response history given an extreme wave match in time, with time reversed for one of the signals. This relationship will provide an efficient and robust way of defining a ‘designer wave’, for both experimental testing and computationally intensive computational fluid dynamics (CFD), for a wide range of wave–structure interaction problems.