钝体表面附着物对低速水流压电俘能器性能影响研究
EFFECT OF ATTACHMENT FOR BLUFF BODY SURFACE ON PIEZOELECTRIC ENERGY HARVESTER PERFORMANCE IN LOW VELOCITY WATER FLOW
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摘要: 低速水流能可作为可再生能源的重要补充, 适用于低速水流能开发的压电俘能器已在流场中表现出了优异的性能. 而在钝体的表面增加附着物可影响压电俘能器的能量转换. 通过改变附着物的形状、凸起高度和凹陷深度探究其对驰振式压电俘能器输出特性的影响. 利用拓展的哈密顿原理建立俘能器的机械控制方程, 引入高斯定理建立电场−位移控制方程, 并基于准稳态假设计算驰振的水动力及力矩, 进而得到压电俘能器机电耦合分段参数模型. 用伽辽金法离散悬臂梁的位移, 并在此基础上解耦控制方程, 从而得到输出功率及悬臂梁位移近似解. 通过水槽实验获得压电俘能器输出功率的实验值, 并验证了数学模型的准确性. 结果表明: 0.51 m/s流速下, −2 mm椭球型凸起的压电俘能器RMS功率为1.411 mW, 与无附着物的椭圆柱相比增幅为69.88%; 当钝体包裹6 mm凸起的圆柱型附着物时, 悬臂梁末端的振幅为3.07 mm, 相比于无附着物的情况降低了84.83%. 三维数值模拟的结果表明凸起、凹陷为2 mm附着物的应用会使在钝体上形成的压差升高, 进而加剧流致振动, 且会影响从钝体两侧脱落涡的大小及强度.Abstract: Low velocity water flow energy is an important complement to renewable energy and the piezoelectric energy harvesters developed by using this energy have shown excellent performance in flow fields. The energy conversion of piezoelectric energy harvesters can be affected by the added attachments on bluff body surface. Therefore, the output characteristics of the piezoelectric energy harvester are investigated by varying the shape, the convexity height and the concavity depth of the attachment. Mechanical governing equation of the piezoelectric energy harvester is developed by using the extended Hamilton’s principle, the electric field-displacement governing equation is obtained by applying Gauss law, the quasi-steady-state assumption is employed to calculate the hydrodynamic force and moment of galloping, and then the electromechanical coupling piecewise distributed parameter model of the piezoelectric energy harvester is established. The displacement of the cantilever beam is discrete by Galerkin procedure, and the governing equations are decoupled on this basis to obtain the approximate solution of harvester output power and bluff body displacement. Experimental solutions of the output power are obtained by water channel experiment and the accuracy of model is further verified. The results showed that at the flow velocity of 0.51 m/s, the RMS power of the piezoelectric energy harvester wrapped ellipsoidal attachment with −2 mm convexity is 1.411 mW, an increase of 69.88% compared to the elliptic cylinder without attachment, and the amplitude of cantilever beam is 3.07 mm when the bluff body is equipped on the cylindrical attachment with 6 mm convexity, a reduction of 84.83% compared to the one without the attachment. The numerical simulation results show that the application of the convex and concave attachment for 2 mm increases the pressure differential across bluff body, which intensifies vibration, it also affects the size and strength of shedding vortices from both sides of the bluff body.