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| 1 | Third generation of vortex identification methods:Omega and Liutex/Rortex based systems显示文摘A vortex is intuitively recognized as the rotational/swirling motion of fluids,but a rigorous and universally-accepted definition is still not available.Vorticity tube/filament has been regarded equivalent to a vortex since Helmholtz proposed the concepts of vorticity tube/filament in 1858 and the vorticity-based methods can be categorized as the first generation of vortex identification methods.During the last three decades,a lot of vortex identification methods,including 0,A,and Aci criteria,have been proposed to overcome the problems associated with the vorticity-based methods.Most of these criteria are based on the Cauchy-Stokes decomposition and/or eigenvalues of the velocity gradient tensor and can be considered as the second generation of vortex identification methods.Starting from 2014,the Vortex and Turbulence Research Team at the University of Texas at Arlington(the UTA team)focus on the development of a new generation of vortex identification methods.The first fruit of this effort,a new Omega(/2)vortex identification method,which defined a vortex as a connected region where the vorticity overtakes the deformation,was published in 2016.In 2017 and 2018,a Liutex(previously called Rortex)vector was proposed to provide a mathematical definition of the local rigid rotation part of the fluid motion,including both the local rotational axis and the rotational strength.Liutex/Rortex is a new physical quantity with scalar,vector and tensor forms exactly representing the local rigid rotation of fluids.Meanwhile,a decomposition of the vorticity to a rotational part namely Liutex/Rortex and an anti-symmetric shear part(RS decomposition)was introduced in 2018,and a universal decomposition of the velocity gradient tensor to a rotation part(7?)and a non-rotation part(NR、was also given in 2018 as a counterpart of the traditional Cauchy-Stokes decomposition.Later in early 2019,a Liutex/Rortex based Omega method called Omega-Liutex,which combines the respective advantages of both Liutex/Rortex and Omega methods,was developed.And a latest objective Omega method,which is still under development,is also briefly introduced.These advances are classified as the third generation of vortex identification methods in the current paper.To elaborate the advantages of the third-generation methods,six core issues for vortex definition and identification have been raised,including:(1)the absolute strength,(2)the relative strength,(3)the rotational axis,(4)the vortex core center location,(5)the vortex core size,(6)the vortex boundary.The new third generation of vortex identification methods can provide reasonable answers to these questions,while other vortex identification methods fail to answer all questions except for the approximation of vortex boundaries.The purpose of the current paper is to summarize the main ideas and methods of the third generation of vortex identification methods rather than to conduct a comprehensive review on the historical development of vortex identification methods. | Chaoqun Liu Yi-sheng Gao Xiang-rui Dong Yi-qian Wang Jian-ming Liu Yu-ning Zhang Xiao-shu Cai Nan Gui | 2019 | Journal of Hydrodynamics2019，31，2： | 82 |
| 2 | Liutex (vortex) core definition and automatic identification for turbulence vortex structures显示文摘As a milestone research in vortex identification(VI),the physical quantity of Liutex,including its forms of scalar,vector and tensor,was systematically explored and rigorously obtained as the third-generation(3G)of the vortex definition and identification methods distinguished from the first generation(1G)by vorticity and the second generation(2G)by the vortex identification(VI)criteria solely dependent on the velocity gradient tensor eigenvalues.Based on these findings,the vortex-core lines were abstracted from the well-defined Liutex,and for the first time,were automatically generated and massively visualized using computer.The distinctive characteristics of these vortex cores with the intriguing threshold-independency make them be the uniquely appropriate entity to represent and to depict the vortex structures in turbulence.The letter made use of the DNS data for the natural transition in a zero-pressure gradient flat-plate(Type-A turbulent boundary layer(TBL))and the fully-developed turbulence in a square annular duct(Type-B TBL)to demonstrate the vortex structure represented by the vortex-core lines.The 3G VI approach based on the vortex-core lines is capable of profoundly uncovering the vortex natures.Moreover,the capability of automatically identifying the vortex cores and massively visualizing the large number of vortex-core behaviors in a transient way will enable the fluid-mechanics and other related-science communities to step into a new era to explore the intrinsic natures of the centennial puzzle of turbulence and other vortex-related phenomena in future. | Hongyi Xu Xiao-shu Cai Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，5： | 21 |
| 3 | A Liutex based definition and identification of vortex core center lines显示文摘Six core issues for vortex definition and identification concern with (1) the absolute strength,(2) the relative strength,(3) the rotational axis,(4) the vortex core center,(5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the criterion and the Acj criterion etc., are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient. | Yi-sheng Gao Jian-ming Liu Yi-fei Yu Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，3： | 19 |
| 4 | Identification of Lagrangian coherent structures in the turbulent boundary layer显示文摘Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor- tices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im- plemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y+=100. The ensem- ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla- tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(y) ac- cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down- stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond. | PAN Chong WANG JinJun ZHANG Cao | 2009 | Science China(Physics,Mechanics & Astronomy)2009，52，2： | 14 |
| 5 | Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods显示文摘Cavitation is a complex multiphase flow phenomenon with an abrupt transient phase change between the liquid and the vapor, including multiscale vortical motions. The transient cavitation dynamics is closely associated with the evolution of the cavitation vortex structures. The present paper investigates the cavitation vortex dynamics using different vortex identification methods, including the vorticity method, the Q criterion method, the Omega method (Ω), the method and the Rortex method. The Q criterion is an eigenvalue-based criterion, and in the Ω method, the parameter is normalized, is independent of the threshold value and in most conditions Ω= 0.52 . The Rortex method is based on an eigenvector-based criterion. Numerical simulations are conducted using the implemented compressible cavitation solver in the open source software OpenFOAM for the sheet/cloud cavitating flows around a NACA66 (mod) hydrofoil fixed at a = 6°,= 1.25 and Re = 7.96 × 10^5 . The flow is characterized by the alternate interactions of the re-entrant flow and the collapse induced shock wave. Results include the vapor structures and the vortex dynamics in the unsteady sheet/cloud cavitating flows, with emphasis on the vortex structures in thecavitation region, the cavity interface, the cavity closure, the cavity wakes, and the foil wakes with the shedding cavity. The comparisons of the various methods, including that the vorticity method, the Q criterion method, the Ω method, the λ2 method and the Rortex method, show the performances of different methods in identifying the cavitation vortex structures. Generally, during the attached cavity growth stage, the Q criteria can well predict the vortex structures in the cavitation region and at the foil trailing edge in the pure liquid region, while with the Ω method and the Rortex method, the vortex structures outside the attached cavity and on the foil pressure side can also be predicted. The λ2 method can well predict the vortex structures in the cavity closure region. During the re-entrant jet development stage, the vortex structures in the re-entrant jet region is weak. During the cavity cloud shedding stage, the vortex dynamics at the foil leading edge covered by newly grown cavity sheet is different from that during the attached cavity sheet growth stage. During the shock wave formation and propagation stage, strong vortex structures with both the size and the strength are observed owing to the cavity cloud shedding and collapse behavior. The influence of the small parameter ε in the Ω method on the cavitation vortex identification is discussed. | Chang-chang Wang Ying Liu Jie Chen Fu-yi Zhang Biao Huang Guo-yu Wang | 2019 | Journal of Hydrodynamics2019，31，3： | 12 |
| 6 | Comparisons and analyses of vortex identification between Omega method and Q criterion显示文摘The present paper presents comparisons of the vortex identification between the Omega method and the Q criterion based on the data of a classical flow.From the comparisons of the vortex structure together with the flow statistics,some important conclusions are drawn on the validity of the two methods,as follows.The Omega method can identify various kinds of vortices with different intensities(e.g.,the strong vortex,the medium vortex and the weak vortex).For the Q criterion,due to the subjective threshold selection,only the strong vortex with weak deformations could be identified.Finally,some emerging topics related with the advanced vortex identification methods are briefly discussed. | Yu-ning Zhang Xiao-yu Wang Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，2： | 8 |
| 7 | The applicability of vortex identification methods for complex vortex structures in axial turbine rotor passages显示文摘The complex vortex structures in the flow around turbine rotor passages, with weak or strong, large or small vortices, interacting with each other, often generate most of aerodynamic loss in turbomachines. Therefore, it is important to identify the vortex structures accurately for the flow field analysis and the aerodynamic performance optimization for turbomachines. In this paper, by using 4 vortex identification methods (the Q criterion, the Q method, the Liutex method and the Q -Liutex method), the vortices are identified in turbine rotor passages. In terms of the threshold selection, the results show that the D method and the Q -Liutex method are more robust, by which strong and weak vortices can be visualized simultaneously over a wide range of thresholds. As for the display consistency of the vortex identification methods and the streamlines, it is shown that the Liutex method gives results coinciding best with the streamlines in identifying strong vortices, while the Q -Liutex method gives results the most consistent with the streamlines in identifying weak vortices. As to the relationship among the loss, the vortices and the shear, except for the Q criterion, the other three methods can distinguish the vortical regions from the high shear regions. And the flow losses in turbine rotor passages are often related to high shear zones, while there is a small loss within the core of the vortex. In order to obtain the variation of vortices in the turbine rotor passages at different working points, the Liutex method is applied in 2 cases of a turbine with different angles of attack. The identification results show that the strengths of the tip leakage vortex and the upper passage vortex are weaker and the distance between them is closer at a negative angle of attack. This indicates that the Liutex method is an effective method, and can be used to analyze the vortex structures and their evolution in turbine rotor passages. | Yu-fan Wang Wei-hao Zhang Xia Cao Hong-kai Yang | 2019 | Journal of Hydrodynamics2019，31，4： | 8 |
| 8 | Galilean invariance of Omega vortex identification method显示文摘In the new vortex identification method(Liu et al.2016)to represent the rotation level and capture and visualize the vortices,proposed in our previous study,the independence of the reference frame and the Galilean invariant were not proved.In the present study,the Galilean invariance of the omega vortex identification method is proved and several examples are presented to verify the conclusion. | Jian-ming Liu Yi-qian Wang Yi-sheng Gao Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，2： | 6 |
| 9 | Application of Omega vortex identification method in cavity buffeting noise显示文摘The cavity buffeting noise is related to the free shear layer oscillation and the periodic vortex shedding,where weak vortices coexist with strong vortices and the strong shear phenomenon also exists at the opening of the cavity.Therefore,it is of great significance to accurately capture vortices at the opening for the control of the cavity buffeting noise.This paper first compares the Omega vortex identification method with the Q andλ2criteria based on the large eddy simulation(LES)of the backward-facing step flow,and it is found that the Omega method enjoys the following advantages:it is not sensitive to a moderate threshold change andΩ=0.52 can be used as a fixed threshold,it can capture both the strong and weak vortices at the same time;and it will not be contaminated by the shear.Then the Omega(Ω)method is applied to the LES of the cavity buffeting noise:the mechanism of the cavity buffeting noise is studied based on a simple cavity model firstly,and then the effects of the incoming boundary layer thicknesses and the incoming boundary layer shapes on the cavity buffeting noise are analyzed.The results show that:theΩmethod clearly captures the processes of the vortex generation,development,collision and fragmentation,verifying that the generation of the cavity buffeting noise is related to the free shear layer oscillation and the periodic vortex shedding;as the thickness of the incoming boundary layer increases,the free shear layer becomes more stable and the Helmholtz resonance is avoided effectively,thereby the cavity buffeting noise is reduced effectively,adding a convexity upstream of the cavity opening to interfere the shape of the incoming boundary layer to reduce the acoustic feedback effect can reduce the cavity buffeting noise effectively. | Yang-hui Zhang Xing-jun Hu Wei Lan Yi-chen Liu Mo Wang Jing-yu Wang | 2021 | Journal of Hydrodynamics2021，33，2： | 3 |
| 10 | Extension Omega and Omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow显示文摘The vortex structure plays a significant role in the investigation of the turbulent drag reduction effect of the viscoelastic turbulent flow.This paper aims to find out an optimal vortex identification method for the viscoelastic turbulent flows,and then studies the turbulent drag reduction mechanism by analyzing the characteristics of the identified vortex structures in the turbulent flows of the viscoelastic fluids.The Q,λ2,Liutex,Omega(Ω)and Omega-Liutex(ΩR)methods are adopted for the identification of vortex structures in the forced homogeneous isotropic turbulence(FHIT)with/without the polymer additive,respectively.The comparison among these five methods shows that the threshold values for the Q,λ2 and Liutex methods should be specially adjusted so as to suitably describe the strong and weak vortex structures in the FHIT of both the Newtonian and viscoelastic fluids,while a fixed threshold value of 0.52 for theΩandΩR methods is effective for both the Newtonian and viscoelastic fluids.The comparison between the identified vortex structures in the FHIT with and without the polymer additive indicates that theΩandΩR methods are more appropriate for the vortex identification because their dimensionless values with a fixed range from 0 to 1 can avoid the effect of the different ranges of the Q,λ2 and∣R∣(for the Liutex method)for the Newtonian and viscoelastic fluids.This also illustrates that theΩandΩR methods can be extended to identify the vortex structures in the turbulent flow of the viscoelastic fluid.Finally,the characteristics of the vortex structures in the FHIT of the viscoelastic fluid are analyzed by utilizing theΩandΩR methods.The results show that both the strong and weak vortex structures are inhibited by increasing the concentration of the polymer solution and by decreasing the Weissenberg number,especially for the weak vortex structures. | Lu Wang Zhi-ying Zheng Wei-hua Cai Wan-you Li | 2019 | Journal of Hydrodynamics2019，31，5： | 2 |
| 11 | Objective Omega vortex identification method显示文摘A new vortex identification method (Liu et al. 2016) was proposed to represent the rotation relative strength and capture and visualize the vortices in our previous study. The basic idea of the Ω method is that a ratio of the vorticity squared over the summation of the vorticity squared and the deformation squared should be used to measure the relative rotation strength. However, the vorticity tensor norm is not objective. Thus, a moving observer will observe different vortex structures in a moving reference frame, which will make confusions about the real vortex structures. In the present study, by the definitions of the net spin tensor and the net vorticity vector, an objective Ω vortex identification method is presented with examples to verify that the vortex structures retain in a moving reference frame. | Jian-ming Liu Yi-sheng Gao Yi-qian Wang Chaoqun Liu | 2019 | Journal of Hydrodynamics2019，31，3： | 0 |
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