﻿ 三维水翼片空泡尺度效应研究
 舰船科学技术  2016, Vol. 38 Issue (12): 30-34 PDF

1. 海军工程大学 船舶与动力学院, 湖北 武汉 430033 ;
2. 海军装备部驻上海沪东中华造船(集团)有限公司军事代表室, 上海 200000

Scaling effects of hydrofoil sheet cavitation
PU Ji-jun1, XIONG Ying1, ZHAO He-yu2
1. College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033, China ;
2. Naval Military Representative Office in Hudong-zhonghua Shipbuilding(group) Co., Ltd., Shanghai 200000, China
Abstract: LES model were conducted in the analysis of hydrofoil sheet cavitation scaling effects. The shedding procedure of sheet cavitation in one circle is simulated. The CFD results is compared with experiment in detail and it is found that LES results which can clearly show the whole shedding procedure of sheet cavitation is agreed well with experiment. The influences of velocity and model size to sheet cavitation are studied, it is found the velocity can barely affect the sheet cavitation inception number and model size has some effect on sheet cavitation, but the effect is not big. Based on that, new scaling law of sheet cavitation inception number is deduced.
Key words: hydrofoil     sheet cavitation     scaling effects
0 引 言

1 数值方法 1.1 LES 湍流模型

LES 的控制方程为：

 $\frac{{\partial \overline {{u_i}} }}{{\partial t}} + \frac{{\partial \overline {{u_i}{u_j}} }}{{{x_i}}} =-\frac{1}{\rho }\frac{{\partial \overline p }}{{\partial {x_i}}} + \nu \frac{{{\partial ^2}\overline {{u_i}} }}{{\partial {x_i}\partial {x_j}}} + \frac{{\partial \overline {{\tau _{ij}}} }}{{\partial {x_j}}},$ (1)

 $\overline {{\tau _{ij}}} = {L_{ij}} + {C_{ij}} + {R_{ij}},$ (2)

 ${L_{ij}} = (\overline {{u_i}} \overline {{u_j}}-\overline {\overline {{u_i}} \overline {{u_j}} } ),$ (3)
 ${C_{ij}} = (\overline {\overline {{u_i}} u_j^{''}}-\overline {\overline {{u_j}} u_i^{''}} ),$ (4)
 ${R_{ij}} =-\overline {u_i^{''}u_j^{''}} {\text {。}}$ (5)

1.2 Zwart et al 空泡模型

 $R = n \times \left( {4\pi R_B^2{\rho _v}\frac{{D{R_B}}}{{Dt}}} \right),$ (6)

 $R = \frac{{3\alpha {\rho _v}}}{{{R_B}}}\sqrt {\frac{2}{3}\frac{{{P_B}-P}}{{{\rho _l}}}},$ (7)

PPv 时：

 ${R_e} = {F_{vap}}\frac{{3{\alpha _{nuc}}(1-{\alpha _v}){\rho _v}}}{{{R_B}}}\sqrt {\frac{2}{3}\frac{{{P_B}-P}}{{{\rho _l}}}}\text{，}$ (8)

PPv 时：

 ${R_c} = {F_{cond}}\frac{{3{\alpha _v}{\alpha _v}{\rho _v}}}{{{R_B}}}\sqrt {\frac{2}{3}\frac{{{P_B}-P}}{{{\rho _l}}}} {\text {。}}$ (9)

2 计算模型和网格划分

 $\alpha (\overline z ) = {\alpha _{\max }}\left( {2{{\left| {\overline z } \right|}^3}-3{{\overline z }^2} + 1} \right) + {\alpha _{wall}}{\text {。}}$ (10)

 图 1 三维扭曲水翼和计算流域 Fig. 1 Geometry of 3D twisted hydrofoil and domain used in computations

 图 2 计算网格图 Fig. 2 Overall view of computational domain grid
3 水翼空泡模拟

 图 3 （a）,（c）,（e）,（g）,（i）为单周期内LES计算结果；（b）,（d）,（f）,（h）,（j）为试验结果 Fig. 3 (a), (c), (e), (g), (i) are LES results of one shedding cycle, (b), (d), (f), (h), (j) are videos of image

1）第 1 阶段（图 3（a）图 3（b））。此时片空泡以达到最大尺寸，空泡边线处出现许多微小气泡（由于网格密度的问题，CFD 模拟中不能捕捉到该气泡），同时，在片空泡的尾端处已出现小范围空隙，该空隙在 LES 计算结果中也有清楚的显示。

2）第 2 阶段（图 3（c）~图 3（f））。此时由于回射流的影响，完整的片空泡被逐渐分割开来，尾端小块的空泡开始聚集起来并发生初次脱落。一般认为回射流位于气穴下方，在空泡体积未达到最大时便已出现，是导致空泡脱落的重要原因[7]。脱落的空泡因压力原因逐渐稀释变为雾状空泡并慢慢消失。

3）第 3 阶段（图 3（g）~图 3（j）。当初次脱落完成后，附着片空泡在尾端的左右两侧开始发生二次脱落，脱落过程与初次脱落相似，但脱落的空泡体积较小。在二次脱落完成以后，片空泡的体积开始逐渐增大，开始进入下一脱落周期。

4 片空泡尺度效应研究 4.1 速度影响研究

 ${V_{vap}} = \sum\limits_{i = 1}^N {{\alpha _i}} {V_i}{\text {。}}$ (11)
4.2 尺寸影响研究

 图 4 初始片空泡数尺度效应图 Fig. 4 Size scale effect of sheet cavitation inception number

 ${\sigma _i} = a \cdot {e^{bx}} + c \cdot {e^{dx}}{\text {。}}$ (12)

abcd 的具体值如表 2 所示。

 图 5 片空泡尺度效应图 Fig. 5 Size scale effect of sheet cavitation

5 结 语

1）LES 湍流模型的计算结果与实验结果吻合较好，不仅能模拟出空泡形成的准确区域，还清楚完整的显示了片空泡的脱落过程，包括初次脱落、二次脱落以及空泡雾化等具体细节。

2）虽然来流速度的变化显著的影响着片空泡生成的临界压力值，但从总体上来说，空泡数保持在一个相对稳定的范围内，可以得出结论：来流速度对初始片空泡数基本无影响。

3）除对产生水蒸汽的含量有较高要求的领域外，尺寸的改变对片空泡的形成和发展有影响，但该影响并不大。总的来说，片空泡的尺度效应影响较小。

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