﻿ 非正弦升沉运动下串列水翼推进性能研究
 舰船科学技术  2022, Vol. 44 Issue (18): 94-100    DOI: 10.3404/j.issn.1672-7649.2022.18.019 PDF

Research on the propulsive performance of the non-sinusoidal plunging in-line tandem hydrofoils
LI Guang-zhao, CHANG Xin, DENG Nan-yan, YU Peng-yao
College of Naval Architecture and Ocean Engineering, Dalian Maritime University, Dalian 116026, China
Abstract: In order to explore the influence of non-sinusoidal motion on the propulsion performance of in-line tandem hydrofoil, this paper adopts computational fluid dynamics method and overlapping grid technology to establish a two-dimensional hydrodynamic numerical model under pure plunge motion of in-line tandem hydrofoil. The comparison of the numerical results of different time steps and grid sizes verifies the convergence of the numerical model. The calculation accuracy of the numerical model is verified by comparison with published experiments and numerical results. Furthermore, the non-sinusoidal coefficient S is introduced to study the influence of non-sinusoidal motion on the propulsion performance of the in-line tandem plunge hydrofoil. The results show that when the non-sinusoidal coefficient increases or decreases from S=1, the instantaneous peak value of the hydrodynamic force of the tandem hydrofoil increases. Except for the state of motion under individual phase differences, the average thrust coefficient of the front and rear wings increases under non-sinusoidal motion. Compared with sinusoidal motion, reducing the non-sinusoidal coefficient can increase the propulsion of the front and rear wings effectiveness.
Key words: in-line tandem hydrofoil     non-sinusoidal motion     plunge motion     computational fluid dynamics     propulsion efficiency
0 引　言

1 计算方法 1.1 扑翼运动的描述

 $h(t) = {h_0}\frac{{S\cos (\omega t)}}{{\sqrt {{S^2}\cos {{(\omega t)}^2} + \sin {{(\omega t)}^2}} }}。$ (1)

 图 1 不同S值的扑翼运动轨迹 Fig. 1 Flapping trajectories according to different values of S

 ${h_1}(t) = {h_0}\frac{{S\cos (\omega t)}}{{\sqrt {{S^2}\cos {{(\omega t)}^2} + \sin {{(\omega t)}^2}} }}，$ (2)
 ${h_2}(t) = {h_0}\frac{{S\cos (\omega t - \varepsilon )}}{{\sqrt {{S^2}\cos {{(\omega t - \varepsilon )}^2} + \sin {{(\omega t - \varepsilon )}^2}} }}。$ (3)

 图 2 串列水翼布置图 Fig. 2 Layout of in-line tandem hydrofoils
1.2 物理量的定义

 ${C_T} = \frac{{{F_X}(t)}}{{\dfrac{1}{2}\rho c{U^2}}}，$ (4)
 ${C_Y} = \frac{{{F_Y}(t)}}{{\dfrac{1}{2}\rho c{U^2}}}。$ (5)

 ${C_{T,mean}} = \dfrac{{\dfrac{1}{T} \displaystyle \int_0^T {{F_X}(t){\rm{d}}t} }}{{0.5\rho c{U^2}}}，$ (6)
 ${C_{P,mean}} = \frac{{{P_{input}}}}{{0.5\rho c{U^3}}}。$ (7)

 ${P_{input}} = \frac{1}{T}\displaystyle \int_0^T {{F_Y}(t) \cdot v(t)} {\rm{d}}t。$ (8)

 $\eta = \frac{{{C_{T,mean}}}}{{{C_{P,mean}}}}。$ (9)
1.3 数值方法与计算模型

 图 3 串列双翼计算域及边界条件 Fig. 3 The domain and boundary conditions of in-line tandem hydrofoils
1.4 数值收敛性分析

 $Re = \frac{{Uc}}{v}。$ (10)

 $St = \frac{{2{h_0}f}}{{{U_0}}}。$ (11)

 图 4 不同时间步长下瞬时推力系数时历曲线 Fig. 4 Time history of instantaneous thrust coefficient of in-line tandem flapping foil under different time steps

 图 5 不同网格下的瞬时推力系数时历曲线 Fig. 5 Time history of instantaneous thrust coefficient of in-line tandem flapping foil under different grids
1.5 数值算法的验证

 图 6 单翼升沉运动验证 Fig. 6 Plunge motion verification of single hydrofoil

 图 7 串列双翼复合运动验证 Fig. 7 Combined motion verification of in-line tandem hydrofoils
2 结果与分析

2.1 非正弦升沉系数S对瞬时水动力的影响

 图 8 不同非正弦系数下串列扑翼的瞬时推力系数时历 Fig. 8 Time history of instantaneous thrust coefficients of in-line tandem flapping foils under different non-sinusoidal coefficient

 图 9 不同非正弦系数下串列扑翼的瞬时升力系数时历 Fig. 9 Time history of instantaneous lift coefficients of in-line tandem flapping foils under different non-sinusoidal coefficient
2.2 非正弦升沉系数S对涡结构的影响

 图 10 前翼运动至最大负向位移位置处(t=0.5T)的涡量云图 Fig. 10 The vorticity contour of the forefoil moving to the position of maximum negative displacement (t=0.5T)

 图 11 后翼运动至平衡位置处（t=0.5T）的涡量云图 Fig. 11 The vorticity contour of the hindfoil moving to the equilibrium position (t=0.5T)

2.3 非正弦升沉系数S对推进表现的影响

 图 12 前后翼在不同相位差下，扑翼推进表现随非正弦系数的变化 Fig. 12 Under different phase differences, the propulsion performance of the fore and hind foils changes with the non-sinusoidal coefficient

3 结　语

1）通过不同时间步长和网格尺寸的数值结果比较，验证了数值模型的收敛性；通过与公开发表试验和数值结果的比较，验证了数值模型的计算精度。

2）非正弦升沉运动相比于正弦升沉运动会增大扑翼的瞬时推力峰值和升力峰值，而且，非正弦系数S的量值与S=1的偏差越大，瞬时峰值增大程度越明显。

3）非正弦系数可以改变水翼表面涡的脱落模式，当S<1时，一组尾涡由2个旋向相同、一个旋向相反的涡组成；当S>1时，一组尾涡由2对旋向相反的涡组成。

4）除个别少数相位差对应的运动状态，与正弦运动相比，当非正弦系数从S=1增大或减小时，非正弦运动下的前翼和后翼平均推力增大。

5）除个别少数相位差对应的运动状态，与正弦运动相比，当非正弦系数从S=1增大时，前翼和后翼的推进效率减小；当非正弦系数从S=1减小时，前翼和后翼的推进效率增大。除此之外，在此基础上改变双翼相位差可以进一步使串列水翼达到最佳推进效率，这将为串列双翼水下航行器推进系统的设计提供指导。

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