﻿ 三维摆动水翼仿生推进水动力分析
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 应用科技  2019, Vol. 46 Issue (2): 1-6  DOI: 10.11991/yykj.201809017 0

### 引用本文

HU Jian, ZHAO Wang, WANG Zibin. Hydrodynamic analysis of 3D flapping hydrofoil bionic propulsion[J]. Applied Science and Technology, 2019, 46(2), 1-6. DOI: 10.11991/yykj.201809017.

### 文章历史

Hydrodynamic analysis of 3D flapping hydrofoil bionic propulsion
HU Jian, ZHAO Wang, WANG Zibin
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: In order to observe the distribution of surface pressure and influence of the convection field in the three-dimensional oscillating hydrofoil movement, taking the NACA0012 airfoil with the NACA airfoil and the aspect ratio of 1.5 as an example, the hydrodynamic characteristics of the swinging hydrofoil were analyzed by computational fluid dynamics. In order to improve the mesh quality, the computational field was divided into the motion field containing the flapping foil, the wake field containing the flapping hydrofoil and the rest field other than the former two fields. These three parts were dispersed under different grid partitioning condition. Solve the discrete equation by k−ω turbulence model, apply the overlapping grid method to simulate the static domain and fluid domain, and use the interface technology to realize data transmission. Analyze the thrust, lift and moment of the oscillating hydrofoil under different St number condition, study the velocity and pressure distribution in the flow field, and analyze the mechanism generating wake vortex by numerical results.
Keywords: flapping foil    three-dimensional    St    wake vortex    NACA0012    overlapping grid    computational fluid dynamics

1971年，Lighthill[4]提出了“大摆动细长体理论”，考虑了尾翼任意摆动幅度的运动，侧向位移较大，并对鱼的运动状态进行了分析。在1977年，Chopra等[5]提出了一种可用于摆动和新月形尾鳍推进系统的“二维抗力理论”，在理论上，尾鳍和摆动运动被充分考虑，并分析了任意摆动的规则或不规则运动，得到了推动力的表达式、维持运动所需的螺旋桨功率等，并指出水动力效率是斯特罗哈尔数（St数）、振幅的函数。

Wu[6]在1961年提出了二维波板理论，在这个理论中，鱼的身体被认为是一个弹性薄板，然后利用二维波片理论研究鱼体的变速运动。在20世纪80年代，中国科技大学的童秉刚等[7]建立了3D WPT理论，运用这一理论对不同种类鱼类的泳姿进行研究，以选择最佳的推进方式。在此期间，他们加入边界层来分析基于半解析理论的大摆幅运动问题。

1 理论基础 1.1 基本方程

 \left\{ \begin{aligned} & \frac{{\partial \rho }}{{\partial t}} + \nabla (\rho V) = 0 \\ & \frac{{\partial (\rho V)}}{{\partial t}} + \nabla (\rho VV) = \rho {{f - }}\nabla p + \nabla \tau \\ & \mathop c\nolimits_p \left[ {\frac{{\partial (\rho T)}}{{\partial t}} + \nabla (\rho VT)} \right] = \frac{{Dp}}{{Dt}} + \varphi + \nabla \& (k\nabla T) + S \\ & p = \rho RT \end{aligned} \right.

 $\varphi = \nabla (\tau \cdot V) - (\nabla \tau )\cdot V$

 \left\{ \begin{aligned} & \tau = - \frac{2}{3}\mu (\nabla V)I + 2\mu S\\ & S = \frac{1}{2}\left[ {{{(\nabla V)}_c} + (\nabla V)} \right] \end{aligned} \right.

 \left\{ \begin{aligned} & \nabla V = 0 \\ & \frac{{\partial V}}{{\partial t}} + V \cdot \nabla V = {{f}} - \frac{1}{\rho }\nabla p + \frac{1}{\rho }\nabla \tau \\ \end{aligned} \right.

1.2 湍流方程

 \left\{ \begin{aligned} & \frac{{\partial k}}{{\partial t}} + {u_i}\frac{{\partial k}}{{\partial {x_i}}} = \frac{1}{\rho }{P_k} - {\beta '}k\omega +\frac{1}{\rho }\frac{\partial }{{\partial {x_i}}}\left[ {\left( {{\mu _i} + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial k}}{{\partial t}}} \right] \\ & \frac{{\partial \omega }}{{\partial t}} + {u_i}\frac{{\partial \omega }}{{\partial {x_i}}} = \frac{1}{\rho }{P_\omega } - \beta {\omega ^2} + \\ & \quad \quad \frac{1}{\rho }\frac{\partial }{{\partial {x_i}}}\left[ {\left( {{\mu _i} + \frac{{{\mu _t}}}{{{\sigma _\omega }}}} \right)\frac{{\partial \omega }}{{\partial {x_i}}}} \right] + 2(1 - {F_1})\sigma {\omega _2}\frac{1}{\omega }\frac{{\partial k}}{{\partial {x_i}}}\frac{{\partial \omega }}{{\partial {x_i}}} \\ \end{aligned} \right.

 ${\mu _t} = \min \left[ {\frac{{\rho k}}{\omega }, \frac{{{a_1}\rho k}}{{\varOmega {F_2}}}} \right]$

 $\varphi = {F_1}{\varphi _1} + \left( {1 - {F_1}} \right){\varphi _2}$
2 数值模型建立 2.1 计算模型及网格

2.2 运动条件

 \left\{ \begin{aligned} & y\left( t \right) = {y_0}\cos \left( {wt} \right) \\ & \theta \left( t \right) = {\theta _0}\cos \left( {wt{\rm{ + }}\phi } \right) \\ \end{aligned} \right.

 $S \!\! t = \frac{{fA}}{U}$

3 数值结果分析 3.1 摆动水翼表面压力分布

3.2 力的曲线

3.3 尾涡的生成

4 结论

1）摆动水翼上方和下方交替出现高压区域，摆动水翼上下的压力差产生推水的效果；

2）当平移幅值、水流进速和俯仰角度幅值都固定不变时，水动力性能随St数的变化而变化，最大推力、最大升力和最大力矩都随着St数的增大而增加；

3）推力、升力和力矩曲线都呈现周期性规律，这与摆动翼的运动规律有关，摆动翼的运动模型是用三角函数表示的运动，由此导致了尾涡在波峰和波谷出现，尾涡的反卡门涡街式的排列使得摆动水翼产生了推力。

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