﻿ 基于CFD的对转螺旋桨水动力性能分析
 舰船科学技术  2019, Vol. 41 Issue (2): 36-40 PDF

1. 武汉理工大学 能源与动力工程学院，湖北 武汉 430063;
2. 国家水运安全工程技术研究中心可靠性工程研究所，湖北 武汉 430063

Hydrodynamic performance analysis of counter-rotating propellers based on CFD
SUN Cheng-liang1,2, ZHAO Jiang-bin1,2
1. School of Energy and Power Engineering, Wuhan University of Technology, Wuhan 430063, China;
2. Reliability Engineering Institute, National Engineering Research Center for Water Transport Safety (WTS), Wuhan 430063, China
Abstract: SolidWorks and Ansys were used for propeller modeling and hydrodynamic calculation respectively based on RANS. The open water performance of propeller was calculated under three different turbulence models, and the results showed that SST model fited best with test value, which was the optimal turbulence model. Through the study of the pitch ratio and diameter ratio of counter-rotating propellers, the optimum value was obtained, and in this case the open water efficiency of counter-rotating propellers is the highest, then it was verified by the wake analysis. In order to compare with equivalent single propeller hydrodynamic performance of the counter-rotating propeller, the equivalent single propeller model was built, under the same power coefficient comparison, results showed that the counter-rotating propeller had obvious advantages in terms of efficiency.
Key words: counter-rotating propellers     CFD     hydrodynamic performance     turbulence model
0 引　言

1 螺旋桨基本参数

2 CFD计算原理 2.1 控制方程及湍流模型

 $\frac{{\partial {u_i}}}{{\partial {x_i}}} = 0{\text{，}}$ (1)
 $\rho \frac{{\partial \left( {{u_i}{u_j}} \right)}}{{\partial {x_j}}} = - \frac{{\partial P}}{{\partial {x_j}}} + \rho {g_i} + \rho \frac{\partial }{{\partial {x_j}}} \cdot \left[ {\mu \left( {\frac{{\partial {u_i}}}{{\partial x}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right) - \overline {{{u'}_i}{{u'}_j}} } \right]{\text{。}}$ (2)

 $\begin{split} \frac{{\partial \rho k}}{{\partial t}} + \frac{{\partial \rho ku}}{{\partial x}} + \frac{{\partial \rho kv}}{{\partial y}} + \frac{{\partial \rho kw}}{{\partial z}} = \frac{\partial }{{\partial x}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial k}}{{\partial x}}} \right] +\\ \frac{\partial }{{\partial y}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial k}}{{\partial y}}} \right] + \frac{\partial }{{\partial z}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial k}}{{\partial z}}} \right] + {P_k} - \rho {\beta ^ * }k\omega \hfill{\text{，}} \end{split}$ (3)
 $\begin{split} \frac{{\partial \rho \omega }}{{\partial t}} + \frac{{\partial \rho \omega u}}{{\partial x}} + \frac{{\partial \rho \omega v}}{{\partial y}} + \frac{{\partial \rho \omega w}}{{\partial z}} = \frac{\partial }{{\partial x}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _\omega }}}} \right)\frac{{\partial \omega }}{{\partial x}}} \right] + \\ \!\! \frac{\partial }{{\partial y}}\left[ {\left( {\mu \!+\! \!\frac{{{\mu _t}}}{{{\sigma _\omega }}}} \right)\frac{{\partial \omega }}{{\partial y}}} \right]\! +\! \!\frac{\partial }{{\partial z}}\left[ {\left( {\mu\! +\! \!\frac{{{\mu _t}}}{{{\sigma _\omega }}}} \right)\frac{{\partial \omega }}{{\partial z}}} \right] \!+ \!\!\alpha \frac{\omega }{k}{P_k} - \beta \rho {\omega ^2}{\text{。}}\\ \end{split}$ (4)

 $\begin{split}{P_k} = {\mu _t}{S^2},S = \sqrt {\sum\limits_i {\sum\limits_j {{S_{ij}}{S_{ij}}} } } ,{S_{ij}} = \\ \frac{1}{2}\left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right){\text{。}}\end{split}$ (5)

2.2 对转桨计算公式

 ${\text{前桨}}\left\{ \begin{gathered} J = \frac{{{V_A}}}{{n{D_f}}},{K_{Tf}} = \frac{{{T_f}}}{{\rho {n^2}{D_f}^4}}{\text{，}} \hfill \\ {K_{Qf}} = \frac{{{Q_f}}}{{\rho {n^2}{D_f}^5}},{\eta _f} = \frac{{{K_{Tf}}}}{{{K_{Qf}}}} \cdot \frac{J}{{2{\text{π}}}} \hfill {\text{。}}\\ \end{gathered} \right.$ (6)
 ${\text{后桨}}\left\{ \begin{gathered} {K_T}_a = \frac{{{T_a}}}{{\rho {n^2}{D_f}^4}},{K_Q}_a = \frac{{{Q_a}}}{{\rho {n^2}{D_f}^5}}{\text{，}} \hfill \\ {\eta _f} = \frac{{{K_T}_a}}{{{K_Q}_a}} \cdot \frac{J}{{2{\text{π}}}}{\text{。}} \hfill \\ \end{gathered} \right.$ (7)
 ${\text{对转桨}}\left\{ \begin{gathered} T = \left| {{T_f}} \right| + \left| {{T_a}} \right|,Q = \left| {{Q_f}} \right| + \left| {{Q_a}} \right|{\text{，}} \hfill \\ \eta = \frac{{{K_T}}}{{{K_Q}}} \cdot \frac{J}{{2{\text{π}} }}{\text{，}} \hfill \\ {K_T} = {K_{Tf}} + {K_{Ta}},{K_Q} = {K_{Qf}} + {K_{Qa}}{\text{。}} \hfill \\ \end{gathered} \right.$ (8)
3 计算方法及最佳湍流模型的选择 3.1 建模及网格划分

 图 1 MAU型螺旋桨 Fig. 1 The MAU propeller

 图 2 网格划分及计算域设置情况 Fig. 2 Grid division and computing domain Settings
3.2 最佳湍流模型

 图 3 不同湍流模型计算的敞水特性曲线 Fig. 3 Open water characteristic curves calculated by different turbulence models

4 对转桨数值仿真及分析

 图 4 对转桨模型 Fig. 4 The counter-rotating propeller model

 图 5 网格划分情况 Fig. 5 Computational domain meshing
4.1 桨距比L/D最优值研究

 图 6 不同桨距比下对转桨敞水性能曲线 Fig. 6 The open water performance curves of counter-rotatong propellers under different L/D
4.2 直径比Da/Df最优值研究

 图 7 不同直径比下的对转桨敞水曲线 Fig. 7 The open water performance curves of counter-rotating propellers under different diameter ratio

4.3 尾流分析

 图 8 对转桨尾流线图（J=0.6） Fig. 8 The wake flow of counter-rotating propellers

4.4 对转桨与等效单桨性能对比

 ${B_p} = \frac{{{P_D}^{0.5}n}}{{{V_A}^{2.5}}} = 33.30\frac{{{K_Q}^{0.5}}}{{{J^{2.5}}}}{\text{。}}$ (9)

 图 9 对转桨和单桨的 ${B_p} - {\eta _0}$ 曲线 Fig. 9 The ${B_p} - {\eta _0}$ curves of counter-rotating propellers and the single propeller

5 结　语

1）基于RANS方程，计算得到螺旋桨的敞水性能，并与图谱试验值对比发现，Standard $k - \varepsilon$ ，RNG $k - \varepsilon$ ，SST $k - \omega$ 三种湍流模型中，SST $k - \omega$ 模型的计算误差最小，为最佳湍流模型。

2）通过CFD仿真计算，得到对转桨的最佳配合参数，L/D=0.267，Da/Df=0.94。尾流分析的结果也支持了得到的最佳桨距比和直径比的结果。

3）将对转桨和等效单桨的敞水性能在相同的功率系数下作对比，发现对转桨的效率比单桨最大提高9.307%，从而证明了对转桨的优越性。

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