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Vortex identification based on the Liutex method and its effect on fish passage upstream

Journal of Hydrodynamics 2024年第1期36卷 130-141页

作者： Chun-ying Shen Rui-guo Yang Xiao-tao Shi Ming-ming Wang Shi-hua He Faculty of Electrical Power Engineering Kunming University of Science and TechnologyKunming650500China Hubei International Science and Technology Cooperation Base of Fish Passage China Three Gorges UniversityYichang443002China Shanghai Investigation Design and Research Institute Co.LtShanghai200434China

Fishway research is important for mitigating the fragmentation of river habitats caused by hydraulic projects.The vertical slit fishway is a broadly used fishway type because of its high efficiency and adaptability to water levels.However,the resulting vortex current disrupts the fish passage hence directly affecting fish migration.This study aims to accurately capture the vortex structure in the fishway and analyze the effect of vortex elements(vortex structure,vortex intensity,etc.)on fish.We conducted an analysis of the 3-D current flow field in the fishway through the utilization of an experimental model and the large eddy simulation(LES)method.Moreover,we captured the vortex information in the fishway at different flow rates using the Liutex vortex identification method and investigated the effect of the vortex on fish migration.The results revealed that the structures inside the fishway pool occupy most of the room,however,the areas with higher vortex strength were primarily located in the vortex near the vertical seam and the mainstream,the vortex strength inside the fishway gradually increases with increasing flow,suppressing fish migration.Fish experienced significantly increased resistance when encountering strong vortices.This suggests that the vortex may act as a physical barrier to fish migration.These findings highlight the potential negative effects of vortex on fish movement and reiterate the importance of understanding vortex dynamics for aquatic environmental management.As an effective tool for identifying vortices in fluid flow,the Liutex method demonstrates features of vortex within the fishway,thereby providing important insights into the interaction between fluid dynamics and aquatic organisms.

关键词： Vertical slit fishway vortex identification method Liutex large eddy simulation(LES) fish experiment computational fluid dynamics

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A modified-Liutex-based vortex-core-line extractor and its application

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Journal of Hydrodynamics 2023年第4期35卷 811-824页

作者： Jin-yan Cai Dong Li Zi-ming Xu Ze-yu Zhang Jiao-lin Cui School of Aeronautics Northwestern Polytechnical UniversityXi’an710072China High Speed Aerodynamics Institute China Aerodynamics Research and Development CenterMianyang621000China

Vortices,which appear as swirling behaviour of a flow field,are an important phenomenon in fluid dynamics,and the extraction of vortex cores is necessary for the research of vortex evolution in many areas of fluid mechanics.The Liutex method is a milestone in vortex identification and provides a reasonable mathematical definition for a vortex core.Based on this definition,a novel integration-based method is presented,which can reduce the numerical error in the integration process through location optimization.Two typical test cases,the wake vortices of an A320 in the near-ground stage and a helicopter rotor,are examined to show that the proposed method can extract continuous vortex core lines with accuracy and efficiency for vortex parameter study.

关键词： Vortex definition flow visualization Liutex vortex core lines optimization

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Identification of vortex boundaries in two-dimensional incompressible flows based on the Liutex-shear interaction

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Journal of Hydrodynamics 2023年第5期35卷 825-831页

作者： Bi-yu Pang Zhang-dan Yu Bo-Wen Yan Yi-qian Wang Chaoqun Liu School of Mathematical Sciences Soochow UniversitySuzhou215006China Department of Computer Science and Technology Tsinghua UniversityBeijing100084China Department of Mathematics University of Texas at ArlingtonArlington76019USA

According to the Liutex-shear decomposition,vorticity can be decomposed into a rotational part,i.e.,the Liutex vector,and a residual shear part.With this decomposition,the vorticity transport equation can be used to formulate a governing equation for Liutex easily for two-dimensional incompressible flows with a source term depending on the residual shear.The dynamics of Liutex-identified structures is then studied in a Taylor-Green vortex flow and a flow past a cylinder at Reynolds number of 200.It is revealed that such boundaries exist outside which the shear has trivial impact on the evolution of Liutex and inside which enhancing and weakening effects of shear on Liutex can be observed.In addition,there is a strong dissipation effect upon Liutex on these boundaries.Based on the interaction mechanism between Liutex and shear,we argue that the vortex boundaries can be identified by these highly dissipative boundaries.In contrast,traditional methods use iso-surfaces of arbitrarily selected thresholds to represent vortex boundaries.The current method of identifying vortex boundaries based on the Liutex-shear interaction has a clearer theoretical base and avoids the arbitrary selection of thresholds.Extensions to three-dimensional incompressible flows can be made in future following the same procedure but with a slightly more complex vorticity transport equation which includes the velocity gradient induced stretching or tilting term.

关键词： Vortex boundary identification Liutex residual shear Taylor-Green vortex cylinder flow

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Speculation of fluid dynamics equations based on Liutex theory and constitutive relation of symmetric shearing deformation

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Journal of Hydrodynamics 2023年第4期35卷 607-629页

作者： Shuai-chen Zhu Duo Wang Yang Liu Hongyi Xu Department of Aeronautics and Astronautics Fudan UniversityShanghai200433China

The fluid kinematics of Liutex decomposes a velocity gradient tensor(VGT)of∇v into four components,including rotation(R),stretching/compressing(SC),anti-symmetric shear(Santi-sym)and symmetric shear(Ssym),as oppose to the traditional Cauchy-Stokes decomposition where a VGT was decomposed into the strain rate and vorticity tensors.The current study limpidly clarified the physical meanings of these deformations in the newly-proposed decomposition from the perspectives of both fluid kinematics and dynamics.With in-depth understanding the physical connotations of these deformations,the present study further suggests that the Ssym be the only deformation appropriately correlated to the stress tensor,leading to the establishment of a new constitutive relation for Newtonian fluids with the modified model assumptions originated from Stokes in 1845.Moreover,the present research finds that the“principal decomposition”proposed by Liu is not mathematically unique when a VGT has three real eigenvalues(TR).Within the context,a new decomposition method is introduced to avoid the non-uniqueness issue arising from using the principal decomposition to establish fluid dynamics equations.Based on the modified Stokes assumptions and the novel VGT decomposition method,a set of new fluid dynamics momentum equations are obtained for Newtonian fluid.The added stress tensor of Fadd is identified as the key difference between the newly-derived governing equations and the conventional Navier-Stokes(N-S)equations,which is caused by excluding the SC correlation to the stress tensor in the new constitutive equation.Finally,a preliminary analysis of Fadd is conducted using the existing channel turbulence direct numerical simulations(DNS)data based on the traditional N-S equations.The Fadd is found widely existing in turbulence and is of the same order of magnitude with the other force terms.Therefore,the Fadd is expected to have some nonnegligible effects on altering the current DNS data based on the traditional N-S equations,which will be furt

关键词： Constitutive relation Liutex principal decomposition Newtonian fluid Navier-Stokes equations fluid kinematics fluid dynamics

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A Liutex-based subgrid stress model for large-eddy simulation

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Journal of Hydrodynamics 2022年第6期34卷 1145-1150页

作者： Yuan Ding Bi-yu Pang Bo-wen Yan Yi-qian Wang Yu-xuan Chen Yue-hong Qian School of Mathematical Science Soochow UniversitySuzhou215006China Department of Computer Science and Technology Tsinghua UniversityBeijing100084China

The concept of vortex is crucial in both understanding and modeling of turbulence.For large eddy simulation(LES),the effect of small-scale eddies onto the large scales or the resolved flow field is modeled by subgrid stress models.Even though the rotating motions of fluids,i.e.,vortices or eddies are central in developing turbulent models,vortex identification methods are seldom used in these models.In this study,we develop a new subgrid model based on the Liutex vector,a new quantity introduced to decompose fluid motions into rigid rotation,pure shear and stretching,and thus identify vortices.The new model is then applied in a decaying homogeneous isotropic turbulence(DHIT)and a turbulent channel flow at Reynolds number Reτ=180.It is shown that the new model can predict accurate energy spectra compared with experiments in DHIT and give a well-matched velocity profile in turbulent channel flow without changing the form of the model.Future directions include improvement of the Liutex based model,for example developing anisotropic subgrid models,and its applications in various turbulent flows.

关键词： Liutex large eddy simulation(LES) subgrid model homogeneous isotropic turbulence turbulent channel flow

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NACA0018翼型锯齿格尼襟翼尾迹特征的Liutex分析

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太阳能学报 2022年第10期43卷 210-217页

作者：于永迪陈榴郑哲辉戴韧上海理工大学能源与动力工程学院上海200093 上海市动力工程多项流动与传热重点实验室上海200093

在雷诺数Re=1.38×10^(5)时,采用实验测量对比研究NACA0018原始翼型以及带有格尼襟翼和齿形襟翼翼型的尾迹涡结构,对比锯齿襟翼与格尼襟翼的控制机理。结果表明,在小攻角下,锯齿襟翼较格尼襟翼大大降低尾迹速度亏损,但速度偏转小于格尼... 详细信息

在雷诺数Re=1.38×10^(5)时,采用实验测量对比研究NACA0018原始翼型以及带有格尼襟翼和齿形襟翼翼型的尾迹涡结构,对比锯齿襟翼与格尼襟翼的控制机理。结果表明,在小攻角下,锯齿襟翼较格尼襟翼大大降低尾迹速度亏损,但速度偏转小于格尼襟翼。通过Liutex分析发现气流经过锯齿襟翼后产生了对涡结构,与襟翼固有的流向涡掺混耗散,削弱由于流向涡引起的尾流不稳定性,从而减小翼型的阻力。对比齿形结构不同位置处的流动表明,在尾缘附近,速度偏转角从齿根,齿中到齿尖依次增加,对于远场的尾迹,3个截面的流动一致。

关键词：风力机流动控制尾迹涡锯齿格尼襟翼 Liutex

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Mathematical foundation of Liutex theory

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Journal of Hydrodynamics 2022年第6期34卷 981-993页

作者： Chaoqun Liu Yifei Yu Department of Mathematics University of Texas at ArlingtonArlingtonTexas76019USA

Liutex is a mathematical definition of vortex,which is called the third generation of vortex definition and identification.This paper introduces the mathematical foundation of the Liutex theoretical system including differences in definition and operations between tensor/vector and matrix.The right version of velocity gradient tensor matrix is given to correct the old version which has been widely distributed by many mathematics and fluid dynamics textbooks.A unique velocity gradient principal matrix is provided.The mathematical foundation for Liutex definition is given.The coordinate rotation(Q-and P-rotation)for principal coordinate system and principal matrix is derived,which is the key issue of the new fluid kinematics.The divergence of velocity gradient tensor is given in different forms which may be beneficial in developing new governing equations for fluid dynamics.

关键词： Liutex mathematical foundation tensor matrix velocity gradient fluid dynamics

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Liutex based new fluid kinematics

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Journal of Hydrodynamics 2022年第3期34卷 355-371页

作者： Chaoqun Liu Yifei Yu Yi-sheng Gao Department of Mathematics University of Texas at ArlingtonArlingtonTexas76019USA College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing210016China

The traditional Cauchy-Stokes(C-S)decomposition states that the velocity gradient tensor can be decomposed into a symmetric tensor and an anti-symmetric tensor,namely the strain-rate tensor and the vorticity tensor.However,there are two problems with the C-S decomposition.One is that the anti-symmetric(vorticity)tensor cannot represent the fluid rotation or vortex.Another is that the symmetric(strain-rate)tensor cannot distinguish the stretching/compression and shear.Since vorticity cannot distinguish between the non-rotational shear and the rigid rotation,vorticity has been decomposed into a rigid rotation part called“Liutex”and an anti-symmetric shear in our previous work.A Liutex-based principal coordinate system has been proposed,and the corresponding velocity gradient tensor decomposition,called the principal decomposition,is presented in this principal coordinate system,which results in:(1)a Liutex tensor that represents rigid rotation,(2)a tensor that represents pure shear and(3)a tensor that represents stretching/compression.However,each point has its own principal coordinate system,which implies that the principal decomposition is performed in different principal coordinate systems,not the original(global)coordinate system.To address this issue,the principal decomposition in the original coordinate system is derived in this paper,and,therefore,provides a new kinematic approach to study the local rigid rotation,pure shear,and stretching/compression.The principal decomposition is unique,Galilean invariant and has clear physical meaning.The new velocity gradient tensor decomposition could become a foundation for new fluid kinematics.

关键词： Liutex principal coordinates principal decomposition Helmholtz Cauchy-Stokes(C-S)

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Numerical study of the near-wall vortical structures in particle-laden turbulent flow by a new vortex identification method-Liutex

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Journal of Hydrodynamics 2024年第1期36卷 53-60页

作者： Farid Rousta Goodarz Ahmadi Bamdad Lessani Chaoqun Liu Department of Mechanical and Aerospace Engineering Clarkson UniversityPotsdamNYUSA Mechanical Engineering and Engineering Science The University of North Carolina at CharlotteCharlotteNCUSA Department of Mathematics University of Texas at ArlingtonArlingtonTXUSA

This study investigates turbulent particle-laden channel flows using direct numerical simulations employing the Eulerian-Lagrangian method.A two-way coupling approach is adopted to explore the mutual interaction between particles and fluid flow.The considered cases include flow with particle Stokes number varying from St=2 up to St=100 while maintaining a constant Reynolds number of Reτ=180 across all cases.A novel vortex identification method,Liutex(Rortex),is employed to assess its efficacy in capturing near-wall turbulent coherent structures and their interactions with particles.The Liutex method provides valuable information on vortex strength and vectors at each location,enabling a detailed examination of the complex interaction between fluid and particulate phases.As widely acknowledged,the interplay between clockwise and counterclockwise vortices in the near-wall region gives rise to low-speed streaks along the wall.These low-speed streaks serve as preferential zones for particle concentration,depending upon the particle Stokes number.It is shown that the Liutex method can capture these vortices and identify the location of low-speed streaks.Additionally,it is observed that the particle Stokes number(size)significantly affects both the strength of these vortices and the streaky structure exhibited by particles.Furthermore,a quantitative analysis of particle behavior in the near-wall region and the formation of elongated particle lines was carried out.This involved examining the average fluid streamwise velocity fluctuations at particle locations,average particle concentration,and the normal velocity of particles for each set of particle Stokes numbers.The investigation reveals the intricate interplay between particles and near-wall structures and the significant influence of particles Stokes number.This study contributes to a deeper understanding of turbulent particle-laden channel flow dynamics.

关键词： Turbulent channel flow particle-laden flow direct numerical simulation(DNS) Eulerian-Lagrangian vortex identification turbulence coherent structures Liutex

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A letter for objective Liutex

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Journal of Hydrodynamics 2022年第5期34卷 965-969页

作者： Yifei Yu Yi-qian Wang Chaoqun Liu Department of Mathematics University of Texas at ArlingtonArlingtonTexas76019USA School of Mathematical Science Soochow UniversitySuzhou215006China

Vortex structures,detected by the existing popular vortex identification methods,of the same case are generally different if the results are measured by different observers,who are moving with different coordinate systems.These coordinate systems can be inertial or non-inertial.Galilean invariance can solve the moving observer problems in different inertial coordinate systems.A variable is invariant under Galilean transformation is called Galilean invariant.Galilean invariant vortex identification methods can provide invariant vortex structures based on different inertial observers.However,for some situations,the observers are non-inertial,e.g.,the observer is sitting on an aircraft which is accelerating or rotating.In such a situation,it requires to use an objective method.Objectivity represents a property that one variable is not observer-dependent(the observer’s motion can be either inertial or non-inertial).A strategy based on a zero-vorticity(measured in inertial frame)reference point is proposed in this letter to find the objective vortex structure.Liutex is chosen as the vortex indicator and two numerical examples are used to test the proposed strategy.The results show that the strategy is effective.

关键词： Objective Liutex vortex structure Galilean invariance

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