VORTEX IDENTIFICATION TECHNOLOGY AND ITS APPLICATION IN THE WAKE FIELD OF MARINE PROPELLER
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摘要: 涡识别是很重要的流体问题, 为了在船用螺旋桨伴流场中寻找一种合理的涡识别方法, 本文结合实践, 研究了六种涡识别技术理论, 其中使用Burgers涡流和Lamb-Oseen涡流作了必要的解释, 讨论了各种识别方法的优缺点. 局部低压标准比较直观, 但深究其黏性和非定常影响后, 明显不足; 迹线或流线显然不能满足伽利略不变性, 会使辨别变得混乱; 涡度大小需要规定其阈值, 具有一定不确定性, 且也会识别不是涡的涡片; 速度梯度张量的复特征值也会有识别不出的区域; 速度梯度张量的第二不变量标准和对称张量的第二特征值标准能更好地识别涡核, 这两种标准有时等效. 螺旋桨伴流场的数值模拟是在开源软件OpenFOAM平台上实现的, 湍流大涡模型由一种局部动态方程建模, 此模型优于动态Smagorinsky模型. 最终的结果显示: 对于船用螺旋桨伴流场中的涡, 采用速度梯度张量的第二不变量和对称张量的第二特征值的结果基本一致, 而最小压力标准、流线或迹线标准、涡度值标准和速度张量的复特征值标准都存在一定的缺陷, 不适用于船用螺旋桨伴流场中的涡识别.Abstract: Vortex identification is a very important problem of fluid and flow, in order to find a reasonable method of vortex identification in the wake of marine propeller, this paper studies the theory of six kinds of vortex recognition technology combined with practice, in which analytic solutions of both Burgers vortex and Lamb-Oseen vortex are also used for necessary explanation. The advantages and disadvantages of various vortex identification methods are discussed in detail at the angle of theory and application. The local low-pressure criterion is intuitive, but it is obviously insufficient after considering viscous and unsteady effects. The path line or streamline criterion obviously cannot satisfy Galileo invariance, which will cause confusion in vortex identification. The magnitude of vorticity criterion needs to specify its threshold value, which has certain uncertainty, and can also incorrectly identify vortex sheets that are not vortices. The complex eigenvalue of the velocity gradient tensor will also have an unrecognized region. The second invariant criterion of the velocity gradient tensor and the second eigenvalue criterion of the symmetric tensor can better identify the vortex core, and these two criteria are sometimes equivalent. The numerical simulation of propeller wake is implemented on the open source software OpenFOAM platform. The large eddy model is modeled by a local dynamic equation, which is better than the dynamic Smagorinsky model to a certain extent. The results of numerical experiment show that, for the vortex identification in the marine propeller wake, the second invariant criterion of the velocity gradient tensor is consistent with the second eigenvalue criterion of the symmetric tensor. However, the local minimum pressure criterion, streamline or path line criterion, vorticity magnitude criterion and complex eigenvalue criterion of velocity gradient tensor have some defects, which are not suitable for vortex identification in the wake of marine propeller.
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Key words:
- vortex identification /
- marine propeller /
- wake field /
- large eddy simulation
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图 2 叶片沿径向相对弦长和扭角分布
Figure 2. Distributions of relative chord length and twist angle along radial direction
图 5 相对涡度和压力分布(实线为涡度, 虚线为压力, 黑虚线为
$ {\omega }_{0} = 1 $ , 向下橙紫绿黄蓝$ {\omega }_{0} $ 分别为$ 2,3, \cdots ,6 $ )Figure 5. Relative vorticity and pressure distribution (solid line is vorticity; dotted line is pressure; black dotted line is
$ {\omega }_{0} = 1 $ ; downward orange-purple-green-yellow-blue lines are$ {\omega }_{0} = 2,3, \cdots, 6 $ respectively)
图 6 Lamb-Oseen涡在不同参考系下的流线(快速点比任何一点的速度都快)
Figure 6. Streamline of vortex under different reference systems (the speed at the fast point is faster than that at any point)
图 9 涡核识别
$ {\lambda }_{2} = 0 $ Figure 9. Vortex core identification
$ {\lambda }_{2} = 0 $ 表 1 涡识别方法
Table 1. Methods of vortex identification
No. Criterions of identifying vortex 1 local minimum pressure 2 pathline or streamline 3 vorticity magnitude 4 complex eigenvalue of tensor $ \boldsymbol{T} $ 5 second invariant $ {\boldsymbol{Q}} $ or kinematic vorticity number $ {N}_{k} $ 6 eigenvalue of sym tensor $\left({\boldsymbol{S} }^{2} + {\boldsymbol{\varOmega } }^{2}\right)$ 
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表 2 计算区不同域网格尺度
Table 2. Overall cell scales in different regions of computational domain
Cell scales for about total 8.5 million cells Region 0 (background grid) $ 0.125 D $ Region 1 (dashed line) $ 0.015\;6 D $ Region 2 (most refinement) $ 0.007\;81 D $
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表 3 基于负
$ {\lambda }_{2} $ 和正$ Q $ 标准识别涡核对比Table 3. Comparison of vortex core identifing results based on negative
$ {\lambda }_{2} $ and positive$ Q $ criteria$ {\lambda }_{1} $ $ {\lambda }_{2} $ $ {\lambda }_{3} $ $\displaystyle \sum {\lambda }_{\mathrm{i} }$ $ -{\lambda }_{2} $ $ + Q $ $ + $ $ - $ $ - $ $ - $ yes yes $ + $ $ - $ $ - $ $ + $ yes no $ + $ $ + $ $ - $ $ - $ no yes $ + $ $ + $ $ + $ $ + $ no no
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