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 应用科技  2017, Vol. 44 Issue (4): 5-11  DOI: 10.11991/yykj.201607010 0

### 引用本文

HU Jian, GUO Lei, LI Conghui, et al. Hydrodynamic performance analysis of hydrofoil in the vicinity of free surface[J]. Applied Science and Technology, 2017, 44(4), 5-11. DOI: 10.11991/yykj.201607010.

### 文章历史

Hydrodynamic performance analysis of hydrofoil in the vicinity of free surface
HU Jian, GUO Lei, LI Conghui, ZHANG Weipeng, LU Zunqi
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: To simulate the viscous flow around a hydrofoil advancing in the vicinity of free surface, the Reynolds averaged Navier-Stokes (RANS) equation is solved numerically using finite volume method. The semi-implicit linked equations consistent (SIMPLEC) algorithm is employed for pressure-velocity coupling. When using volume of fluid (VOF) method to capture the interface, the air and liquid are taken as one type of fluid with different density. At first, the numerical scheme developed in this study was validated through the comparison between the present results and the experimental data. Then, extensive simulation was performed on the wave excitation, pressure distribution and hydrodynamic force of the hydrofoil. Some interesting phenomena, such as the wave rolling, were also discussed. It can be seen from the numerical results that the closer the distance between the surface and the hydrofoil, the smaller the lift and drag of hydrofoil, and the free surface effect can be neglected if the distance is larger than four times of the chord length of the hydrofoil.
Key words: hydrofoil    numerical simulation    interfacial flow    computational fluid dynamics(CFD)    viscous fluid    wave rolling    volume of fluid    free surface of liquid

1 数值理论 1.1 控制方程

 $\begin{array}{l} \frac{\partial }{{\partial t}}\left( {\rho \mathit{\boldsymbol{u}}} \right) + \nabla \cdot \left( {\rho \mathit{\boldsymbol{u}} \otimes \mathit{\boldsymbol{u}}} \right) = \nabla \cdot \left( {\mu \nabla \otimes \mathit{\boldsymbol{u}}} \right) - \nabla \rho + \rho \mathit{\boldsymbol{g}}\\ \quad \quad \quad \quad \quad \quad \quad \nabla \cdot \mathit{\boldsymbol{u}} = 0 \end{array}$

1.2 湍流模型

k-ε双方程模型是目前黏性流场使用最为广泛的模型。该模型又分为标准k-ε模型、RNG k-ε模型和Realizable k-ε模型3种。

 $\begin{array}{l} \frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho k{u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial k}}{{\partial {x_j}}}} \right] + \\ \quad \quad \quad {G_k} + {G_b} - \rho \varepsilon - {Y_M} + {S_k} \end{array}$

 $\begin{array}{l} \frac{{\partial \left( {\rho \varepsilon } \right)}}{{\partial t}} + \frac{{\partial \left( {\rho \varepsilon {u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial \varepsilon }}{{\partial {x_j}}}} \right] + \\ \quad \quad {G_{1\varepsilon }}\frac{\varepsilon }{k} + \left( {{G_k} + {C_{3\varepsilon }}{C_b}} \right){C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k} + {S_k} \end{array}$

1.3 自由界面追踪方法

1.3.1 流体体积分数求解和运动界面捕捉

1.3.2 CICSAM格式运动界面重构

Ubbink和Issa[10]的Compressive Interface Capturing Scheme for Arbitrary Meshes(CICSAM)格式是利用了精细的网格内界面的迁移方法得到的。通过设置法向量为网格内运动界面法向的直线对界面位置进行逼近，若设的界面法向量为n=(n1, n2)，则新构成的界面是n1x+n2y=α的形式。然后通过几何关系可以补充求解α需要的额外方程，然后求解联立方程就可确定出界面的位置了。

 $\begin{array}{l} \quad \quad \quad {C_f} = (1 - {\beta _f}){C_D} + {\beta _f}{C_A}\\ (C_p^{t + \delta t} - C_p^t){V_p} = - \sum\limits_{f = 1}^n {\frac{1}{2}} ({({C_f}{F_f})^t} + {C_f}F_f^{t + \delta t})\delta t \end{array}$

 ${\beta _f} = \frac{{{{\tilde F}_f} - {{\tilde F}_D}}}{{1 - {{\tilde F}_D}}}$

2 水面下水翼航行兴波模拟 2.1 模型及网格建立

 图 1 计算域模型

 图 2 翼型网格拓扑结构

2.2 NACA0012兴波对比分析

 图 3 层流、湍流兴波对比

 图 4 RNG k-ε湍流模型自由液面结果

 图 5 计算域速度云图
 图 6 翼型表面速度矢量图
2.3 NACA4412对比分析

 ${C_p} = \frac{p}{{\frac{1}{2}\rho {V^2}}}$

 $\begin{array}{l} {C_L} = \frac{L}{{\frac{1}{2}\rho {V^2}b}}\\ {C_D} = \frac{D}{{\frac{1}{2}\rho {V^2}b}} \end{array}$

 图 7 NACA4412模型结构

 图 8 Fr=1.03, α=5°时NACA4412表面压力分布

 图 9 不同浸深下升力曲线、阻力曲线与升阻比的变化

 图 10 不同浸深下的兴波图形

 图 11 不同攻角下的兴波图形

2.4 破碎波模拟

 图 12 Fr=0.571 1, α=10°, h/c=0.6时的波浪翻卷

 图 13 翼型表面压力云图

 图 14 翼型表面和自由液面附近的流线图
3 结论

1) 在较为简单的兴波模拟中，层流模型和湍流模型的计算结果同试验结果均吻合较好。其中，层流模型在第1个波峰处拟合较好，而湍流模型由于能量耗散稍大，所以第1个波峰则稍低于实验值，这也是比较合理的，这验证了数值模拟方法的可行性。

2) 通过对非对称翼型NACA4412的计算，根据不同攻角、浸深的对比，从中可以知道兴波的波长不受浸深改变或者翼型攻角变化而变化，但波幅宽度受到的影响较为明显。而在浸深比h/c大于4后，水翼航行基本可以等效为深水，自由表面效应可以忽略。

3) 对NACA4412模型进行数值仿真，很好地模拟了波浪产生破碎瞬间自由液面的演变过程。

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