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基于虚功率原理的鲹科鱼类波状推进分析

黄恺俊 余永亮

黄恺俊, 余永亮. 基于虚功率原理的鲹科鱼类波状推进分析. 力学学报, 2023, 55(7): 1-12 doi: 10.6052/0459-1879-23-076
引用本文: 黄恺俊, 余永亮. 基于虚功率原理的鲹科鱼类波状推进分析. 力学学报, 2023, 55(7): 1-12 doi: 10.6052/0459-1879-23-076
Huang Kaijun, Yu Yongliang. Analysis of carangiform undulation based on virtual power principle. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(7): 1-12 doi: 10.6052/0459-1879-23-076
Citation: Huang Kaijun, Yu Yongliang. Analysis of carangiform undulation based on virtual power principle. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(7): 1-12 doi: 10.6052/0459-1879-23-076

基于虚功率原理的鲹科鱼类波状推进分析

doi: 10.6052/0459-1879-23-076
基金项目: 国家自然科学基金(12172355, 11672291)和中央高校基本科研业务费专项资金(E1E42201)资助项目
详细信息
    作者简介:

    余永亮, 教授, 主要研究方向: 生物运动力学、空气动力学. E-mail: ylyu@ucas.ac.cn

  • 中图分类号: Q352, R318.01

ANALYSIS OF CARANGIFORM UNDULATION BASED ON VIRTUAL POWER PRINCIPLE

  • 摘要: 自然界中的大多数鱼类通过波状摆动的方式实现推进, 这是动态变形的鱼体和周围流体相互作用的结果, 研究推进中流体对鱼体变形的响应不仅可以增强对波状推进的认识, 还可以为流动控制提供依据. 以鲹科模式推进的仿生二维模型为研究对象, 通过数值计算获得鱼体波动产生的流场以及鱼体受到的流体力数据. 基于虚功率原理, 将鱼体受力分解为4部分, 分别是鱼体边界变速运动的瞬时贡献, 流场中流体旋转和应变速率相对大小的贡献, 壁面剪切应力的类摩阻分量和壁面摩阻分量. 结果表明, 当鱼体波状摆动产生推力时, 鱼体边界变速运动是主要的正推力来源, 并且该项80%的推力贡献来源于20%的鱼尾部分的边界变速运动. 鱼尾两侧边界层中的流体旋转和应变速率的相对大小和壁面摩阻对推力都是负贡献. 对于低雷诺数的情况, 流体旋转和应变速率的相对大小的负贡献低于壁面摩阻的负贡献, 而在高雷诺数的情况下, 流体旋转和应变速率的相对大小的负贡献强于壁面摩阻的负贡献. 壁面类摩阻分量相对于其他3项总是较小的. 结合标度律分析, 在摆动推进的标度关系中, 与雷诺数无关的推力部分是由边界的变速运动、流场中流体旋转和应变速率共同提供, 且流体旋转和应变速率也贡献了摆动推力中与雷诺数有关的部分, 而这一部分接近类摩阻和摩阻的一半, 同时, 类摩阻和摩阻还提供了常阻力分量.

     

  • 图  1  仿鱼翼型波状摆动示意图

    Figure  1.  Schematic of a fish-like undulatory airfoil

    图  2  一个波动周期不同时刻的鱼体中心线及其包络线

    Figure  2.  The centerline of the fish body at various time instants for one undulation cycle and their envelops

    图  3  推力系数在一个周期内的变化

    Figure  3.  The time-dependent thrust coefficient in an undulation cycle

    图  4  边界加速度对推力的贡献

    Figure  4.  The contribution of the boundary acceleration

    图  5  $t = 0T,t = 1/8T,t = 1/4T,t = 3/8T $时刻的涡量场(第1列)、Q分布图(第2列)、Q对推力的贡献分布图(第3列)和虚速度势场(第4列)

    Figure  5.  Vorticity field (first column), Q distribution diagram (second column), Q distribution diagram of contribution to thrust (third column) and virtual velocity potential field $\phi $ (fourth column) at $t = 0T,t = 1/8T,t = 1/4T,t = 3/8T $

    图  6  流场分区示意图

    Figure  6.  Schematic of flow field zoning

    图  7  $Q$分布对推力的贡献

    Figure  7.  The contribution of $Q$ distribution to thrust

    图  8  不同尾迹区的$Q$分布对推力的贡献

    Figure  8.  The time-dependent contribution of $Q$ distribution to thrust in different wake regions

    图  9  不同雷诺数$Re$条件下$\left\langle {{C_{T,a}}} \right\rangle ,\left\langle {{C_{T,Q}}} \right\rangle ,\left\langle {{C_{T,v}}} \right\rangle 和\left\langle {{C_{T,f}}} \right\rangle$随运动参数$St$的变化规律

    Figure  9.  The time-averaged thrust coefficient $\left\langle {{C_{T,a}}} \right\rangle ,\left\langle {{C_{T,Q}}} \right\rangle ,\left\langle {{C_{T,v}}} \right\rangle ,\left\langle {{C_{T,f}}} \right\rangle $ as a function of $St$ at different Reynolds number

    图  10  不同雷诺数$Re$条件下$\left\langle {{C_{T,a}}} \right\rangle ,\left\langle {{C_{T,Q}}} \right\rangle ,\left\langle {{C_{T,v}}} \right\rangle 和\left\langle {{C_{T,f}}} \right\rangle$的贡献堆叠柱状图

    Figure  10.  Stacked histogram of the time-averaged thrust coefficient $\left\langle {{C_{T,a}}} \right\rangle ,\left\langle {{C_{T,Q}}} \right\rangle ,\left\langle {{C_{T,v}}} \right\rangle ,\left\langle {{C_{T,f}}} \right\rangle $ at different Reynolds number

    图  11  $t = 0 T,t = 1/8 T,t = 1/4 T和t = 3/8 T$时刻以及不同摆幅条件下($A = 0.06,0.08,0.10,0.12和0.14$), $\Delta \phi (x)$以及$\Delta \phi (x)/A$沿着鱼体中线的分布

    Figure  11.  Distribution of $\Delta \phi (x)$ and $\Delta \phi (x)/A$along the center line of fish at different time($ t = 0 T,t = 1/8 T,t = 1/4 T,t = 3/8 T $) and under different amplitude condition($A = 0.06,0.08,0.10,0.12,0.14$)

    图  12  惯性力对推力贡献的标度关系及其拟合参数与雷诺数的关系

    Figure  12.  Scaling law of the contribution of the inertial force to thrust and the relationship between fitting parameters and Reynolds number

    图  13  内应力对推力贡献的标度关系极其拟合参数与雷诺数的关系

    Figure  13.  Scaling law of the contribution of the internal stress to thrust and the relationship between fitting parameters and Reynolds number

    图  14  鱼体附近动网格示意图

    Figure  14.  Schematic of dynamic meshes near fish body

    图  15  不同网格和时间步长的数值结果比较

    Figure  15.  Comparison of numerical results with different meshes and time steps

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