﻿ 基于 CFD 的喷水推进泵导叶三维反设计研究
 舰船科学技术  2017, Vol. 39 Issue (3): 36-40 PDF

3D inverse design of waterjet stator based on CFD
CHANG Shu-ping, SHI Yan-feng, QIAN Ming-jun, YAO Ding-yuan, LI Kun-peng
No.63969 Unit of PLA, Nanjing 210028, China
Abstract: The bad commutating performance of a waterjet stator is one important reason that the waterjet ship failed to achieve the expected speed. The 3D inverse design method of waterjet stator is introduced, the blade shape is designed for a specified distribution of circulation and meridional geometry. A numerical model based on CFD describing interior flow of waterjet is built up, which is meshed with hexahedral grids and computed by solving RANS equations and SST turbulent model. Ratio of the circumferential energy to the axial energy at nozzle outlet is used to check commutating performance of the stator. The results show that 3D inverse design method and CFD tool can play a important role in waterjet stator design and optimization. The optimized stator largely increases the waterjet thrust about 5%.
Key words: ship     waterjet     stator     inverse design     CFD     circulation
0 引　言

Allison[3] 回顾了喷水推进泵的发展历史，包括一维理论、二维理论和近期发展起来的三维理论及升力面理论，他预言：随着计算机计算能力的提高，泵设计过程中的水动力问题将会更多地采用仿真手段来解决，从而可减少对物理模型的依赖。Tan[4] 提出了一种给定环量分布的三维有势流动计算方法，用置于叶片中心的涡面代替叶片对水流的作用。Borges[5] 在相同设计条件下用常规方法和三维方法设计了 2 个叶轮，结果是三维方法得到的叶轮具有较高的效率和较宽的高效区。Bonaiuti[6] 总结了三维设计中各参数对喷水推进泵的效率和汽蚀性能的影响规律。

1 导叶对喷水推进器推力的影响

 图 1 “喷水推进器+船体”系统[7] Fig. 1 Control volume of waterjet-hull system
 $T = m{V_{out}} - m{V_{in}} = \rho Q({V_{out}} - {V_{in}})\text{，}$ (1)

 $T = \rho Q({V_{out}} - {V_{ship}})\text{。}$ (2)

 $u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial r}} = - \frac{1}{\rho }\frac{{\partial p}}{{\partial x}} + \frac{1}{{\rho r}}\frac{{\partial r{\tau _x}}}{{\partial r}}\text{，}$ (3)

 $\frac{{\partial ru}}{{\partial x}} + \frac{{\partial rv}}{{\partial r}} = 0\text{，}$ (4)

 $\int_0^\infty {\rho u\frac{{\partial u}}{{\partial x}}} r{\rm d}r \!\!+\!\! \int_0^\infty {\rho rv\frac{{\partial u}}{{\partial r}}} {\rm d}r \!=\! - \!\! \int_0^\infty {\frac{{\partial p}}{{\partial x}}r{\rm d}r} \!+\! \!\int_0^\infty {\frac{{\partial r{\tau _x}}}{{\partial r}}} {\rm d}r\text{，}$ (5)

 $\int_0^\infty {\rho u\frac{{\partial u}}{{\partial x}}} r{\rm d}r = \frac{1}{2}\frac{{\rm d}}{{{\rm d}x}}\int_0^\infty {\rho {u^2}} r{\rm d}r\text{，}$ (6)
 $\begin{split}\\[-12pt]\int_0^\infty {\rho vr\frac{{\partial u}}{{\partial r}}} {\rm d}r = \left| {\rho uvr} \right|_0^\infty - \int_0^\infty {\rho u\frac{{\partial (rv)}}{{\partial r}}}{\rm d}r = \\ 0 + \int_0^\infty {\rho u\frac{{\partial (ru)}}{{\partial x}}} {\rm d}r = \frac{1}{2}\frac{{\rm d}}{{{\rm d}x}}\int_0^\infty {\rho {u^2}r} {\rm d}r\text{，}\end{split}$ (7)
 $\int_0^\infty {\frac{{\partial p}}{{\partial x}}} r{\rm d}r = \frac{{\rm d}}{{{\rm d}x}}\int_0^\infty p r{\rm d}r\text{，}$ (8)
 $\int_0^\infty {\frac{{\partial r{\tau _x}}}{{\partial r}}}{\rm d}r = \left| {r{\tau _x}} \right|_0^\infty = 0\text{，}$ (9)

 $\frac{{\rm d}}{{{\rm d}x}}\int_0^\infty {(p + \rho {u^2})} r{\rm d}r = 0\text{。}$ (10)

 $C = \left( {{H_{Vc}}/{H_{Va}}} \right) \times 100\% \text{，}$ (11)

 ${H_{Vc}} = u_c^2/2g\text{，}$ (12)

 ${H_{Va}} = u_a^2/2g\text{。}$ (13)

 图 2 某喷水推进器结构 Fig. 2 A certain waterjet configuration

 图 3 导叶出口的流线 Fig. 3 Streamlines throughout waterjet stator
2 导叶的三维反设计

 ${p^ + } - {p^ - } = \left( {2\rm{\pi} /B} \right)\rho {W_{mbl}}\partial \left( {r{V_\theta }} \right)/\partial m\text{。}$ (14)

3 CFD 数值模型 3.1 控制方程

 $\frac{{\partial \rho }}{{\partial t}} + \nabla \cdot (\rho {V}) = 0$ (15)
 $\frac{D}{{Dt}}(\rho {V}) \!+\! 2\rho {\omega} \!\times\! {V} \!+\! \rho {\omega} \times {\omega} \! \times \! {r} \!=\! \rho {f} \!-\! \nabla P \!+\! (\mu \!+\! {\mu _t}){\nabla ^2} {V}\text{，}$ (16)

 $\frac{D}{{Dt}}(\rho {V} ) = \rho {f} - \nabla P + (\mu + {\mu _t}){\nabla ^2}{V} \text{。}$ (17)
3.2 计算域和网格

 图 5 喷水推进计算域 Fig. 5 Computational domain of waterjet propulsion

 图 6 各部件网格 Fig. 6 Mesh of each part of waterjet
3.3 边界条件

4 导叶的优化设计

MJP 和 KaMeWa 公司的导叶多采用轮毂收缩成一点的形式，本文导叶优化设计也采用了该类结构。若设计航速时通过喷水推进泵的流量与喷水推进泵最高效率点的流量基本一致，可认为“船-泵-机”实现了较好匹配。参照文献[10]，为了优化叶轮通道内二次回流，导叶的载荷分布为轮毂载荷比轮缘载荷更靠前。轮毂流线上 NC，ND 和 SLOPE（SLOPE 为直线斜率）设为 0.15，0.3 和 0.1，轮缘流线上 NC，ND 和 SLOPE 设为 0.45，0.7 和 0.1。图 7 给出了喷口直径为 124 mm 时的叶片形状。图 8 是其内部流线，其周向动能与轴向动能的比值为 0.04，整流效果较原导叶有了大幅提高。

 图 7 喷口直径为 124 mm 时的的导叶形状 Fig. 7 Stator shape with nozzle diameter 124 mm

 图 8 通过喷口直径 124 mm 导叶的流线 Fig. 8 Streamlines throughout the retrofitted stator

 图 9 六型不同喷口直径的轴面轮廓 Fig. 9 Sketch of stator meridional channel

 图 10 不同喷口直径时的流量和推力 Fig. 10 Comparison of mass flow rate and thrust when different nozzle diameters

 图 11 原型导叶与改型导叶的推力对比 Fig. 11 Thrust curves of the original waterjet and the optimized waterjet
5 结　语

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