Century-long Mist on Vortex and Vorticity is Removed by Cooperation of Two Strong Teams

Although vortex is ubiquitous in nature, it is difficult to give a rigorous definition. Helmholtz proposed the concept of “Vortex Filament” in 1858. There are still many textbooks that define vortex as Vorticity Tube. Vorticity magnitude is defined as the strength of the vortex, or the strength of the rotation. It can be clearly seen that in the definition of Helmholtz, the natural phenomenon of fluid rotation (Vortex) and vorticity which is a mathematical definition have been completely equalized, and this confusion has continued to the present with the terms of vortex/vorticity line, vortex/vorticity filament and vortex/vorticity tube. This misunderstanding is challenged as “vortex and vorticity are not well distinguished”.

1. Liutex is born for vortex

In 2017, Professor Chaoqun Liu of the University of Texas at Arlington (UTA) proposed a new physical quantity, Liutex, that represents the fluid rotation or vortex. The main idea is to extract the rigid rotation part out from the fluid motion by using a so-called UTA R-NR decomposition to decompose the velocity gradient tensor into a rotational part R and a non-rotational part NR. It defines the real eigenvector direction of the velocity gradient tensor as the direction of Liutex and twice the rotational angular velocity as the magnitude of Liutex, as shown in Figure 1.

Fig. 1 (a) Liutex vortex core line with isosurface Ω=0.52 (b) Liutex vortex core line, color indicates rotation intensity

Professor Hongyi Xu from Fudan University pointed out:

Xu fully believes that Liutex does lift and uncover the mask covering vortex which has puzzled our science community for so many centuries. Specifically, the Liutex core-lines limpidly bring out the skeleton of vortex structures and for the first time, vividly exhibit these structures to our visual world, which, from Xu’s experience, is so far the unique representation of vortical structures with the true, only true, nothing else but the true mathematical essences of vortex physics in entirety.

Professor Gui Nan from Tsinghua University said:

The Liutex method correctly decomposes the velocity gradient tensor into a rotating part and a non-rotating part, instead of a symmetrical and anti-symmetric parts. There has never been a purely rotating tensor before.

After Liutex was discovered, the team at the University of Texas at Arlington have developed a series of vortex identification methods based on Liutex. Many studies have demonstrated that Liutex core line method can correctly display vortex structures in different flow fields. The programs of these methods can be downloaded for free from the UTA’s website, and everyone is welcome to download, try and use them broadly.

https://www.uta.edu/math/cnsm/public_html/cnsm/cnsm.html

In addition, the UTA team also have proved the existence, uniqueness, stability and Galilean invariance of Liutex. Another very important concept is the “Principal Coordinate”. Because rotation has an axis, it cannot be isotropic. Therefore, at a certain moment, there must be a certain coordinate system which is more important than other coordinate systems. We call this coordinate system the ” Principal Coordinate “. It should be noted that the determination of the ” Principal Coordinate ” is related to the Liutex vector. The Liutex vector may be different at different times, so the ” Principal Coordinate ” is an instant system. The special feature of Principal Coordinate is that the velocity gradient tensor in the Principal Coordinate can be easily decomposed into rotation, stretching and compression, and shearing parts, and the physical meaning of these parts is clear. We call this decomposition “Principal Decomposition”.

Fig.2 The “Principal Decomposition” of the velocity gradient tensor in the “Principal Coordinate”

In fact, vorticity is not only rotation, but rotation plus shear. For solids, the shear is zero or very small, so the vorticity can represent rotation. However, the shear of fluid cannot be ignored, which is a main reason why the vorticity cannot represent the fluid rotation or vortex. Based on the above understanding, Professor Chaoqun Liu proposed the RS decomposition of vorticity. Namely, it is to decompose the vorticity into a rotating part and a shearing part. These theories described above constitute the Liutex theoretical system, which pave the foundation for the new era of vortex science, turbulence research and fluid mechanics.

2. Vortex research has entered a new era

2.1 The third-generation vortex identification methods

The first-generation vortex identification method is based on the vorticity tube, vorticity filament, etc., which is constructed based on the concept of vorticity. However, for parallel shear flow which has no fluid rotation or vortex, there is strong vorticity. Therefore, it is not reliable to detect vortex by vorticity. The second-generation vortex identification methods are based on the eigenvalues ​​of the velocity gradient tensor and related invariants, such as Q, Δ, λ2, and λci. Most of these methods are scalars, thus the information about the direction of the rotation axis is lost. Therefore, only the vortex strength can be qualitatively obtained without the quantity of the angular velocity. For the iso-surface which is the only way can be used to express vortex structure for scalars, the threshold value needs to be artificially adjusted which is some kind arbitrary. In addition, there is also a problem with the wrong order of the dimension. The third generation of vortex identification methods is based on the Liutex. This method does not need to set a threshold. It can not only display the direction of the rotation axis, but also can capture both strong and weak vortices.

2.2 Liutex spectrum discover -5/3 similarity law

After Liutex was proposed, Prof. Liu and his students found that the Liutex (rigid body rotation) spectrum has a -5/3 similarity law in the turbulent boundary layer when they studied an example of Liutex application of DNS for boundary layer transition.

Kolmogorov’s famous -5/3 similarity law is only valid in an inertial subrange of isotropic turbulence with very large Reynolds numbers. It does not fit well with DNS or experimental results in turbulent boundary layers in wall-bounded flows with small and medium Reynolds numbers. However, it can be seen from the Liutex spectrum that the -5/3 similarity law of Liutex agrees very well with DNS!

Fig. 3 The Liutex spectrum has a -5/3 similarity law in the turbulent boundary layer

2.3 Promote vortex science research in the new era

From 2018 to 2019, the UTA team published 13 articles on PoF and more than 14 articles on Journal of Hydrodynamic Series B (JHD). The articles published by the UTA team were ranked as the second, sixth, and seventh 2019 PoF featured letters, the second and fifth 2019 PoF most cited articles, and third and fifteenth 2019 PoF best articles. In addition, Professor Liu and his collaborators published two professional books on Liutex by Bentham and Elsevier.

Fig. 4 Liutex books

3. Cooperation of strong groups to clarify the century long fog of vortex and vorticity

Chaoqun Liu’s UTA ​​team and the Journal of Hydrodynamics are two of the teams dedicated to clarify the misunderstanding of vortex and vorticity. ” Journal of Hydrodynamics ” is an academic journal created by a group of academic predecessors who are interested in the development of hydrodynamics, creatively collecting funds and wisdom in the form of a consortium. ” Journal of Hydrodynamics ” Series A (Chinese Journal) aims at the application, emphasizing the transformation of research and innovative applications in various fields, focusing on domestic communication and increasing domestic influence, and targeting at a goal of becoming the first-class domestic academic journals. “Journal of Hydrodynamics ” series B (Journal of Hydrodynamics, JHD, English) focuses on the frontier and hot research of the subject, eyes at academic level and innovation, aims at international communications and influence, and takes world-class academic journals as a model to pursue. As the journal continuously rising during the past 40 years, a strong editorial boar has been formed with many intelligent and active scientists.

In the discussion about what a vortex is, Prof. Liandi Zhou, the Executive Editor-in-chief, after he summarized many vortex phenomena in nature and had deep discussions with Chaoqun Liu who is the founder of Liutex, proposed the six core elements of vortex. Core elements: (1) the absolute strength of the vortex, (2) the relative strength of the vortex, (3) the local axis of rotation, (4) the center position of the vortex core, (5) the size of the vortex core, (6) the boundary of the vortex.

Prof. Chaoqun Liu uses these six elements as the touchstone for judging various vortex identification methods. Professor Liu pointed out that the first-generation vortex identification method cannot answer any of the aforementioned six elements. The second-generation vortex identification methods cannot answer these elements either except for the approximate vortex boundary by an empirical threshold. So, what is the physical quantity that precisely represents vortex? Professor Chaoqun Liu gave his answer—Liutex. Liutex is a vector, whose magnitude is twice the rotation angular speed and direction is the direction of the local rotation axis. This answers questions (1) and (3); based on the concept of the density of Liutex in the fluid field, Liutex-Omega can be used to measure the relative vortex strength in (2) among the six elements; the center of the vortex itself is a special Liutex line, so the position of the vortex core in (4) can also be answered; through experience, the relative strength of the vortex core can be reduced to 95% to determine the size of the vortex core in (5) and the boundary of the vortex in (6); this method can capture both strong and weak vortices.

A series of studies have demonstrated that Liutex can extract the rigid rotating part from the fluid motion to avoid the contamination of shear. Liutex theory also explains the reason why vorticity is applicable to represent rotation in solids but not in fluids. The theory is that vorticity can be decomposed into the sum of rotation plus shear (this decomposition is called RS decomposition of vorticity). Shear in solids is very small, but the shear in the fluid cannot be ignored. New developments in Liutex theories and methods, such as Liutex vector line, Liutex iso-surface, Liutex-Omega method, Liutex vortex core line, principal coordinate system and Liutex-5/3 similarity law, etc., gradually form a matured Liutex theoretic system.

For an identical goal to develop vortex science and turbulence theory, Chaoqun Liu’s UTA ​​team and JHD promoted their strategic cooperation. The UTA team submitted their new innovative results to JHD in time as their preferred journal, and JHD actively organizes its power to give the priority to the UTA research papers and promotes them in the Springer platform. Only in 2018 and 2019, the UTA team published 12 papers in JHD. The third generation of vortex identification methods is popularized and applied in various fields of hydrodynamics to support and echo the research work of the UTA team. In addition, the JHD editorial board and Prof. Chaoqun Liu’s team have cooperated many times to hold various vortex and turbulence conferences and professionsl meetings to promote the development of Liutex research and increase its influence. Especially during the virus pandemic period in 2020, the Liutex Workshop of the 13th Chaos International Conference, was successfully held. The number of participants reached 35 and 40 papers were presented and discussed, counted as 1/3 of the entire conference participants. The collection of the Liutex Workshop papers was planned to be an edited book “Liutex and Third Generation of Vortex Definition and Identification for Turbulence Research” which is expected to be published by the Springer Nature.

Misunderstanding of vortex and vorticity has lasted for over a hundred years which is deeply rooted. It is of great significance to the development of natural science to correct the chaos and eliminate the fallacy. The two teams, UTA and JHD, have cooperated with each other and complemented each other with their strengths. They are going to clarify this long-lasted misunderstanding and work together to develop Liutex dynamics which is a new highland of scientific research.

References:

[1] Liu C, Gao Y, Dong X, et al. Third generation of vortex identification methods: Omega and Liutex/Rortex based systems[J]. Journal of Hydrodynamics, 2019, 31(2): 205-223.
[2] WANG Yi-qian, GUI Nan, A review of the third-generation vortex identification method and its applications. Chinese Journal of Hydrodynamics, 2019, 34(4), 413-429
[3] Liu Chaoqun, Liutex-Vortex definition and the third-generation vortex identification method Acta Aerodynamics, 2020, 38(3): 413-431.

 

2020年第六届全国船舶与海洋工程CFD专题研讨会 征文通知

2020全国船舶与海洋工程CFD专题研讨会参会回执.doc (116 downloads)

近年来,随着计算机软硬件技术的飞速发展,计算流体动力学CFD技术在船舶与海洋工程领域得到日益广泛而深入的应用。国内相关高等院校、科研院所和船东船厂开展了大量基础性和应用性研发工作,取得了诸多创新成果。

2010年,中国造船工程学会船舶力学学术委员会和中国拖曳水池会议(CTTC)倡议召开“全国船舶与海洋工程CFD专题研讨会”,并由上海交通大学承办了第一届研讨会。此后,2012年由武汉理工大学承办了第二届研讨会,2014年由大连理工大学承办了第三届研讨会,2016年由江苏科技大学承办了第四届研讨会,2018年由中国船舶及海洋工程设计研究院承办了第五届研讨会。第六届全国船舶与海洋工程CFD专题研讨会将于2020年11月27-29日在广州召开,诚邀广大相关学者积极参会。

一、征文范围

本届会议的征文范围涉及但不限于如下CFD应用领域及其相关技术问题:

数值水池、海洋环境模拟、船舶阻力与推进、操纵性与耐波性、波-流-浮体非线性相互作用水动力学及环境载荷、船舶与海洋结构物水弹性与流固耦合、离岸与深海工程结构物水动力性能、水下航行器水动力性能、船舶与海洋工程仿生技术、基于数值模拟的船舶与海洋结构物设计与优化、船舶与海洋工程水动力学问题数值模拟新方法和新技术、空泡与涡流模拟、涡激振动与涡激运动、验证与确认(V&V)、不确定性分析(UA)等。

二、征文要求

请于2020年8月31日前通过电子邮件将论文题目与摘要发至华南理工大学会务组邮箱(cfd2020naoe@163.com),2020年9月30日前提交全文。论文全文经组委会评审通过后,将于2020年10月31日前向作者发出会议邀请函。

所投论文应是尚未公开发表过的,会议论文集将以纸质或电子文档方式提供给会议代表。论文可使用中文或英文撰写。论文应包括论文题目、作者姓名及单位、通讯地址及邮编、联系电话(手机)、E-mail地址、论文摘要、论文内容、参考文献等。征文咨询邮箱:cfd2020naoe@163.com。

组委会将从论文集中评选出部分优秀论文,征得作者同意后,在《中国造船》杂志以专辑增刊形式发表。

主办单位:中国造船工程学会船舶力学学术委员会CFD学组

承办单位:华南理工大学土木与交通学院船舶与海洋工程系

2020年08月5日

以诗情画意之美,增益力学之美;以力学之美,欣赏诗情画意之美

以诗情画意之美,增益力学之美;以力学之美,欣赏诗情画意之美
我国是一个诗词的国度,有灿烂的诗歌文化,唐宋诗词更是我国文学史上一颗璀璨的明珠。古代诗词中有大量对力学现象的精美描写,体现了诗人对力学现象入细入微的观察与力学理性的思考。
通过欣赏古代诗词中对力学现象精湛描述的名篇佳句,将诗情画意与近代力学的发展交融在一起,将科学与艺术融于一体,使欣赏性、知识性、趣味性、科学性巧妙结合,以情、景、声、乐、视、画、图、文并茂的形式,生动鲜明的讲述方式,深入浅出、引人入胜地把力学原理和内在规律介绍给最广大范围的读者。
通过运用力学原理深入浅出地讲解身边的力学现象和力学问题,一方面传播力学知识,同时从诗歌中欣赏力学之美,体验力学趣味,感受力学魅力。以诗情画意之美,增益力学之美;以力学之美,欣赏诗情画意之美。
姜楠教授主讲“诗情画意谈力学”,欢迎大家鉴赏。

北风卷地白草折1

北风卷地白草折2

春蚕到死丝方尽1

春蚕到死丝方尽2

但见流沫生千涡1

但见流沫生千涡2

第五章大风起兮云飞扬——漫话流动显示

飞湍瀑流争喧豗1

飞湍瀑流争喧豗2

风乍起吹皱一池春水1

风乍起吹皱一池春水2

露珠不定始知圆1

露珠不定始知圆2

片花

轻于粉蝶瘦于蜂1

轻于粉蝶瘦于蜂2

野渡无人舟自横1

野渡无人舟自横2

夜半钟声到客船1

夜半钟声到客船2

涡识别应用–Liutex值计算代码下载

Rotex.c (253 downloads)

In the paper “The visualization of turbulent coherent structure in open channel flow” by Bai et al. (2019) -( https://doi.org/10.1007/s42241-019-0026-0 , share this article https://rdcu.be/b457g)

a code the author used is available above.

代码完成功能: 用于计算流场中的Liutex值

用法:同OpenFOAM中vorticity,Q等后处理工具,执行Rotex -case XXX

涡是流体力学中的重要现象,但迄今为止,人们对涡的认识还很模糊,还未能给出一个有物理意义和被广泛接受的定义方法。多年来人们尝试了多种方法,早期曾采用涡量方法,但后来发现涡量和涡结构的关联性不高。后来,又发展了多种以速度梯度张量特征值为代表的涡识别方法,如常用的Q,和等。但这些方法在实际使用过程中,研究者需要不停地调整阈值以获得一个主观确定的等值面效果。从2014年开始,美国德州大学阿灵顿分校的刘超群教授团队提出了涡识别方法和Liutex向量方法。涡识别方法定义为速度梯度张量反对称部分比上对称和反对称部分之和,当比值大于0.5可以认为旋转占优,其应用建议在0.52~0.6之间取值,可使得识别的涡结构基本保持不变。Liutex向量的核心思想是将涡量进一步分解为旋转部分(R)和非旋转部分(S),其中新分解出来的R部分代表流体运动的刚体旋转部分,其认为该空间矢量可用于表征旋涡结构。Liutex 给涡的研究提供了新的视角。

Call For Papers:International Symposium on High-Fidelity Computational Methods & Applications

Dec 14th ~16th, 2019 

Shanghai, China

Introduction & Objective

The original intention of organizing this symposium is to discuss recent advances of the high-fidelity methods and enhance deployment and industrial applications of the methods in complex fluid flows and related topics, which is enlightened by the 4th Nektar++ workshop 2019.

High-fidelity computational methods are emerging tools that underpin science and engineering. Due to the increasingly stringent precision requirements for industrial designs,  these methods have recently attracted even greater attention. This symposium will bring together world leading experts to discuss novel developments, new perspectives and industrial applications. The ultimate goal of the symposium is to expand the range of application of high-fidelity numerical tools in engineering practice.

During the symposium, a Nektar++ tutorial session will be run for the people who are interested in theories of spectral/hp element methods and parallel implementation of the methods. By the tutorial session, people will learn how to use Nektar++ to carry out high-fidelity high-efficient calculations and analyses for incompressible and compressible complex flows and how to write their own customized solvers by virtue of the Nektar++ hierarchical libraries.

Abstracts are invited on the research, application and deployment of high-fidelity methods with a particular interest in computational mathematics, aerodynamics and hydrodynamics.

Some Invited Speakers

Spencer J. Sherwin, FREng, Imperial College London

Pierre Sagaut, Aix-Marseille Université, France

Mike Kirby, University of Utah, USA

Joaquim Peiro, Imperial College London

David Moxey, University of Exeter, UK

Chris Cantwell, Imperial College London, UK

Bruno Carmo, University of São Paulo, Brazil

Sponsors

Imperial College London, UK

Journal of Hydrodynamics, China

Shanghai Jiao Tong University, China

State Key Laboratory of Aerodynamics, China

Science and Technology on Water Jet Propulsion Laboratory, China

Important Dates

Abstract Submission Deadline: Aug. 31, 2019
Abstract Acceptance Notification:    Sept. 15, 2019
Full paper submission (Optional):    Sept. 15, 2019
Paper review & acceptance: Sept. 30, 2019
Registration deadline: Nov. 30, 2019
Paper Presentation: Dec. 14-17, 2019

Papers dealing with any topics within the scope are all invited to be submitted online with an abstract up to 1000 words and figures can be included.

Registration Fee

Registration
Type:
EARLY BIRD
REGULAR
LATE
Before
Oct. 15, 2019
Oct. 16 to
Nov 30, 2019
After Dec. 1, 2019
Participant
600 USD,
3500RMB
700 USD,
4000 RMB
750 USD,
4500 RMB
Student
Participant
300 USD,
1500RMB
350 USD,
2000 RMB
375 USD,
2500 RMB
Accompany
-ing person
300 USD,
1500RMB
350 USD,
2000 RMB
400 USD,
2500 RMB

* Registration and submission should be done online. The website will be ready at the beginning of July. The website link will be mainly disseminated by Editorial board of JHD. Registration will not be completed until the full payment is received.

Conference Schedule

13rd Dec. (Friday), 2019

Registration, Reception, Meeting of executive committees

14th Dec. (Saturday), 2019

Opening ceremony, Invited lectures, Technical sessions, Banquet

15th Dec. (Sunday), 2019

Invited lectures, Technical sessions, Closing ceremony

16nd Dec. (Monday), 2019

Technical Tours

Contact

Hui XU

School of Aeronautics & Astronautics

Shanghai Jiao Tong University

Shanghai 200240, China

Department of Aeronautics

Imperial College London

Exhibition Rd, London SW7 2AZ

E-mail: dr.hxu@sjtu.edu.cn

Phone: +86 152 0219 2258