﻿ 高效扭曲舵的水动力特性数值分析
 舰船科学技术  2023, Vol. 45 Issue (7): 31-34    DOI: 10.3404/j.issn.1672-7649.2023.07.007 PDF

1. 长江大学 文理学院，湖北 荆州 434000;
2. 湖北理工学院，湖北 黄石 435003

Numerical analysis of hydrodynamic characteristics of an efficient twisting rudder
WANG Chun-ge1, HU Chuan-feng2
1. College of Arts and Sciences, Yangtze University, Jingzhou 434000, China;
2. Hubei University of Science and Technology, Huangshi 435003, China
Abstract: Traditional rudder will produce cavitation effect under the influence of ship propeller flow, resulting in the damage of rudder structure and the decrease of steering power, resulting in the increase of ship operation cost. In order to solve this problem, the research on efficient twisting rudder has become a hot topic in the industry. Unlike traditional rudder, torque rudder has better hydrodynamic characteristics and can overcome the influence of ship propeller wake. The research direction of this paper is to carry out theoretical analysis and simulation of hydrodynamic characteristics of efficient twisting rudder, and realize optimal parameter design of twisting rudder, which has certain guiding significance for improving the performance of existing ship rudder.
Key words: twisted rudder     hydrodynamic characteristics     simulation     wake
0 引　言

1 船舶扭曲舵水动力分析的CFD基本理论

 图 1 计算流体力学的有限单元模型 Fig. 1 Finite element model of computational fluid dynamics

1）连续性方程

 $\frac{{\delta V}}{{\delta x}} + \frac{{\delta \left( {\rho l} \right)}}{{\delta x}} + \frac{{\delta \left( {\rho m} \right)}}{{\delta y}} + \frac{{\delta \left( {\rho n} \right)}}{{\delta z}} = 0 \text{，}$

 $\frac{{\delta V}}{{\delta x}} + {\rm{div}}\left( {\sum\limits_{i = 1}^n {{\rho _i}} } \right) = 0 。$

2）能量守恒方程

 $\int\limits_v {\frac{\partial }{{\partial {t^{}}}}\left( {\rho \varphi } \right){\rm{d}}v + \int\limits_{}^{} {{\rm{div}}\left( {\rho \bar \varphi } \right){\rm{d}}v} = } \int\limits_v {S{\rm{d}}v} 。$

 $\rho \frac{{{\rm{d}}\dfrac{1}{2}{V_i}}}{{{\rm{d}}x}} = \frac{\partial }{{\partial x}}\left\{ {\frac{{\delta {{\bar u}_i}}}{{\delta x}}} \right\} + {G_b} - \rho \varepsilon 。$

 $\left\{ {\begin{array}{*{20}{c}} {\dfrac{{\partial E}}{{\partial t}} + {V_i}\dfrac{{\partial k}}{{\partial {x_{}}}} = \dfrac{\partial }{{\partial y}}\left[ {\left( {{\sigma _k}\delta } \right)\dfrac{{\partial E}}{{\partial t}}} \right] + P} \text{，} \\ {\dfrac{{\partial E}}{{\partial t}} + {V_j} = \dfrac{\partial }{{\partial y}}\left[ {\left( {{\sigma _w}\delta } \right)\dfrac{{\partial {E_0}}}{{\partial t}}} \right] + F}。\end{array}} \right.$

3）动量守恒方程

 $M \cdot \frac{\partial }{{\partial t}}\left[ {\delta \left( {\frac{{\partial {V_i}}}{{\partial x}} + \frac{{\partial {V_j}}}{{\partial y}} + \frac{{\partial {V_m}}}{{\partial z}}} \right)} \right] = - \frac{{\partial P}}{{\partial t}} + {F_{}} 。$
2 船舶高效扭曲舵的水动力数值计算分析

 图 2 船舶扭曲舵的剖面力学模型图 Fig. 2 Section mechanical model diagram of ship's twisted rudder

 $P = \sqrt {P_x^2 + P_y^2} 。$

$l$ 为弦长， ${x_t}$ 为压力中心，可求扭曲舵的压力分散系数为：

 $Cp = \frac{{{x_t}}}{l} 。$

 $P = f\left( {{A_k},\alpha ,v,\eta ,\rho ,Re} \right) 。$

 \left\{ {\begin{aligned} &{\dfrac{{\partial {V_m}}}{{\partial {S_m}}} = 0} \text{，}\\ &{\dfrac{{\partial {V_m}}}{{\partial t}} + \dfrac{\partial }{{\partial t}}\left( {{V_m}{S_m}} \right) = - \dfrac{1}{\rho }\dfrac{{\partial {S_m}}}{{\partial t}} + \eta \dfrac{\partial }{{\partial {S_m}}}\left( {\dfrac{{\partial {V_m}}}{{\partial t}}} \right)}。\end{aligned}} \right.

 $\frac{{\partial \left( {\rho {U_x}} \right)}}{{\partial x}} + \frac{{\partial \left( {\rho {U_y}} \right)}}{{\partial y}} + \frac{{\partial \left( {\rho {U_z}} \right)}}{{\partial z}} = 0 。$

 $\frac{{\partial \left( {\rho {V_m}} \right)}}{{\partial t}} + {\rm{div}}\left( {\rho {V_m}} \right) = - \frac{{\partial P}}{{\partial x}} + \frac{{\partial {F_{\tau x}}}}{{\partial x}} + \frac{{\partial {F_{\tau y}}}}{{\partial y}} + \frac{{\partial {F_{\tau z}}}}{{\partial z}} 。$

 $\frac{\partial }{{\partial t}}\left( {\rho lw} \right) + \Delta w \cdot Cp \cdot m\left( {\rho {V_m}} \right) = \Delta w \cdot \psi + {H_\xi } 。$

 $\int {\frac{P}{{{V_m}}}w{\rm{d}}w = \int {\psi \Delta w{\rm{d}}{A_k} + \int_l {{H_\xi }} } } {\rm{d}}w 。$
3 基于Fluent的高效扭曲舵的水动力特性仿真

1）船舵参数的确定

NACA船舵的剖面参数如表1所示。

2）有限元建模

 图 3 扭曲舵表面有限元建模示意图 Fig. 3 Schematic diagram of finite element modeling for twisted rudder surface

3）流场建模

 图 4 扭曲舵计算域流场建模示意图 Fig. 4 Schematic diagram of flow field modeling in the calculation domain of twisted rudder

①入流面的选择

②对称边界

4）属性参数赋值和求解

 图 5 不同仿真边界得到的阻力系数对比 Fig. 5 Comparison of resistance coefficients obtained from different simulation boundaries

4 结　语

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