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

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.

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

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.

Vortex analysis of water flow through gates by different vortex identification methods

The pre-gate suction vortex,gate-bottom-edge transverse vortex,gate-slot vertical vortex,and downstream-of-gate return vortex are important factors affecting the flow instability of flat gates,which may lead to fatigue failure in severe cases.This study used the volume of fluid(VOF)model and large eddy simulation(LES)method to accurately capture the transient turbulence characteristics of flow under different water flow conditions and reveal the flow field and vortex structure.The Q—criterion,Omega(Ω)method,and latest third-generation Liutex vortex identification method were used to analyze and compare the pre-gate suction vortex,gate-slot vertical vortex,and downstream-of-gate return vortex,focusing on the ability of each vortex identification method to capture the flow field information and vortex characteristics.The results reveal that theΩmethod and Liutex method are less dependent on the threshold value,and the Liutex method captures a wide range of pre-gate vortices.Different flow conditions cause changes in the vortex structure of over-gate flow.When the relative opening of the gate is smaller,the intensity of the vortices in the flow field around the gate is greater,the return vortices downstream of the gate are more disordered,and the vortex changes are more violent,which in turn affects the efficient and stable operation of the gate.

Characterization of vortex structures with self-excited oscillations based on Liutex-Omega vortex identification method

The self-excited oscillation effect produces a continuous periodic pulsation without an external excitation source.It is widely used in fluid heat and mass transfer,cavitation and resistance reduction,and other related fields.The self-excited oscillation effect is significantly influenced by the vortex structure created by the jet passing through the specially designed cavity.The flow field in a self-excited oscillation cavity is simulated in this paper using the large eddy simulation(LES)method.The Liutex-Omega([Math Processing Error])method is used to analyze the vortex structure’s evolution inside the cavity and is contrasted with the Q-criterion,the λ_(2)-criterion,and the Omega(Ω)method.The studies indicate that the[Math Processing Error]method is less sensitive to threshold selection compared with other methods,while it is more capable of identifying weak vortices.The change in cavity vortex structure can be devided into the four stages of vortex ring priming,growth and development,wall touch separation,and fragmentation.The turbulent energy generated by shear effect can promote the growth and development of the vortex ring structure and has an important influence on the formation of the vortex ring structure.The vortex strength reveals the interaction mechanism between the shear effect and vortex rings.The vortex core area illustrates that the small-scale vortices are mainly distributed inside the collision walls of the cavity and the downstream flow channel.The Liutex-omega method has unique advantages in analyzing the cavity flow field and revealing the mechanism of self-excited oscillations.

Determination of epsilon for Omega vortex identification method

In the present paper, epsilon（ε） in the Omega vortex identification criterion（ Ω method） is defined as an explicit function in order to apply the Ω method to different cases and even different time steps for the unsteady cases. In our method, e is defined as a function relating with the flow without any subjective adjustment on its coefficient. The newly proposed criteria for the determination of ε is tested in several typical flow cases and is proved to be effective in the current work. The test cases given in the present paper include boundary layer transition, shock wave and boundary layer interaction, and channel flow with different Reynolds numbers.

A selected review of vortex identification methods with applications

In the present review, recent progress on the vortex identification methods are introduced with a focus on the newly proposed omega method（ Ω method）. The advantages of Ω method are summarized with many illustrating examples. Furthermore, comparing with other existing methods（e.g., Q criterion and λ2 criterion）, one of the characteristics of Ω method is its independence on the chosen threshold values for vortex identifications. The important parameters involved for the practical applications of Ω method are further discussed in detail together with the physical interpretation of the Ω and some suggestions of the future work. Other emerging topics（e.g., Lagrangian coherent structure and Rortex） are also introduced with comments.

Analysis of the vortices in the inner flow of reversible pump turbine with the new omega vortex identification method

Reversible pump turbines are widely employed in the pumped hydro energy storage power plants. The frequent shifts among various operational modes for the reversible pump turbines pose various instability problems, e.g., the strong pressure fluctuation, the shaft swing, and the impeller damage. The instability is related to the vortices generated in the channels of the reversible pump turbines in the generating mode. In the present paper, a new omega vortex identification method is applied to the vortex analysis of the reversible pump turbines. The main advantage of the adopted algorithm is that it is physically independent of the selected values for the vortex identification in different working modes. Both weak and strong vortices can be identified by setting the same omega value in the whole passage of the reversible pump turbine. Five typical modes（turbine mode, runaway mode, turbine brake mode, zero-flow-rate mode and reverse pump mode） at several typical guide vane openings are selected for the analysis and comparisons. The differences between various modes and different guide vane openings are compared both qualitatively in terms of the vortex distributions and quantitatively in terms of the areas of the vortices in the reversible pump turbines. Our findings indicate that the new omega method could be successfully applied to the vortex identification in the reversible pump turbines.

Liutex theoretical system and six core elements of vortex identification

The third-generation vortex identification method of Liutex(previously called Rortex)was introduced by the team led by Prof.Chaoqun Liu from University of Texas at Arlington to mathematically extract the rigid rotation part from the fluid motion,and thus to define and visualize vortices.Unlike the vorticity-based first generation and the scalar-valued second generation,Q,λ2,Δandλci methods for example,the Liutex vector provides a unique,mathematical and systematic way to define vortices and visualize vortical structures from multiple perspectives without ambiguity.In this article,we summarize the recent developments of the Liutex framework and discuss the Liutex theoretical system including its existence,uniqueness,stability,Galilean invariance,locality and globality,decomposition in tensor and vector forms,Liutex similarity in turbulence,and multiple Liutex-based vortex visualization methods including Liutex lines,Liutex magnitude iso-surfaces,Liutex-Ωmethod,and Liutex core line method,etc..Thereafter,the six core elements of vortex identification,including(1)absolute strength,(2)relative strength,(3)local rotational axis,(4)vortex rotation axes,(5)vortex core size,(6)vortex boundary,are used as touchstones against which the Liutex vortex identification system is examined.It is demonstrated with illustrative examples that the Liutex system is able to give complete and precise information of all six core elements in contrast to the failure and inaccuracy of the first and second-generation methods.The important concept that vorticity cannot represent vortex and the superiority of the Liutex system over previous methods are reiterated and stated in appropriate places throughout the paper.Finally,the article concludes with future perspectives,especially the application of the Liutex system in studying turbulence mechanisms encouraged by the discovery of Liutex similarity law.As a newly defined physical quantity,Liutex may open a door for quantified vortex and turbulence research including Liutex(vortex)dynamics and lead the community out of the shadow of turbulence research which traditionally relies on observations,graphics,assumptions,hypotheses,and other qualitative analyses.An optimistic projection is that the Liutex system could be critical to investigation of the vortex dynamics in applications from hydrodynamics,aerodynamics,oceanography,meteorology,etc.and to research of the generation,sustenance,modelling and controlling of turbulence.

Vortex identification methods in marine hydrodynamics

In this paper,several commonly used vortex identification methods for marine hydrodynamics are revisited.In order to extract and analyse the vortical structures in marine hydrodynamics,the Q,λ2-criterion and modified normalized Liutex/RortexΩR method are utilized for vortex identification for propeller open water test,ship drag test,ship propeller-rudder interaction,VIV of a marine riser and VIM of a Spar platform.The limitation of Q andλ2-criterion is discussed.The Liutex/RortexΩR method is promising for convenient and accurate vortex identification and visualization.However,care should be taken when choosing the small parameter b0 forΩR.We proposed recommended values of b0 for marine hydrodynamic problems.

New omega vortex identification method

A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and λ_2-method is conducted and the advantages of the new method can be summarized as follows:(1) the method is able to capture vortex well and very easy to perform;(2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and λ_2 chosen to visualize vortices are obscure;(3)being different from Q and λ_2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated;(4) both strong and weak vortices can be captured well simultaneously while improper Q and λ_2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared;(5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow,the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity.

Vortex structures of dynamic pure yaw test using DDES approach and vortex identification method

Considered as the building blocks,vortex structures with variety of sizes and intensity are widely recognized in the viscous flow field around ship.In this paper,the computational fluid dynamics(CFD)solver,naoe-FOAM-SJTU,coupled with delayed detached-eddy simulation(DDES)is adopted to analyze the vortex structures around the benchmark model Yupeng Ship in dynamic pure yaw tests,which are captured by third generation of vortex identification method.The good agreement of the predicted force/moment by DDES method with the experimental data indicates that the present numerical schemes are reliable and robust.Three vortex identification methods,Q-criteria,Ω_(R) and Liutex,are used to capture the vortex structures around the hull.The large separated flow is able to be investigated by these three methods,in which more vortex structures are captured byΩ_(R) approach and Liutex method with scalar,vector and tensor form seems to be more suitable for analyzing the flow mechanism around the hull in dynamic pure yaw test.In general,each vortex structure corresponds to a dominant positive/negative axial Liutex and a bound vortex pair.The streamlines are spiral in the large separated flow,indicating that the flow in corresponding region is rotational.But the rotation of the flow is not directly related to the intensity of Liutex.

On the effectiveness of local vortex identification criteria in the vortex representation of wall-bounded turbulence

Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical vortex-representation notion.This work focuses on the effectiveness of the local identification criteria in the vortex representation of wall-bounded turbulence.Basically,five local identification criteria regarding vortex strength and three criteria for vortex axis are considered.Instead of separately evaluating the two classes of criteria,the current work defines vortex vectors by arbitrarily combining the vortex strength and vortex axis expressed by various criteria,and attempts to figure out the most effective one regarding the vortex representation.The effectiveness of these vortex vectors is evaluated based on two aspects:first,the alignment of the vortex axis and vortex iso-surface should be well established,which benefits the simplification of the vortex filaments;second,vortices could be viewed as the"gene code"of turbulent flows,which means reconstructing the velocity fields based on them should be effective.For the first aspect,the differential geometry method is employed to describe the vortex isosurface-axis alignment property quantitatively.For the second aspect,the Biot-Savart law is employed to accomplish the vortex-to-velocity reconstruction.Results of this work provide some reference for the applications of vortex identification criteria in wall-bounded turbulence.

Physical properties of vortex and applicability of different vortex identification methods

For correct identification of vortices,this paper first analyzes the properties of the rigid vortex core and its induced flow field given by the Rankine vortex model,and it is concluded that the concentrated vortex structure should consist of the vortex core and the induced flow field(the potential flow region with a weak shear layer).Then the vortex structure is analyzed by using the Oseen vortex model.Compared with the Rankine vortex,the Oseen vortex is a concentrated vortex with a deformed vortex core.The vortex structure consists of the vortex core region,the transition region and the shear layer region(or the potential flow region).The transition region reflects the properties of the resultant vorticity of the same magnitude and the resultant deformation rate of the shear layer,and the transition region also determines the boundary of the vortex core.Finally,the evolution of leading-edge vortices of the double-delta wing is numerically simulated.And with different vortex identification methods,the shape and the properties of the leading-edge vortices identified by each method are analyzed and compared.It is found that in the vorticity concentration region,the vortices obtained by using ω,λ2,Ω criteria and Q criteria are basically identical when appropriate threshold values are adopted.However,in the region where the vorticity is dispersed,due to the influence of the flow viscous effect and the adverse pressure gradient,the results obtained by different vortex identification methods can be quite different,as well as the related physical properties,which need to be further studied.

Calibration of S-duct Swirl Distortion Based on Vortex Identification Methods

The S-shape inlet has been widely used in advanced military aircraft due to their advantage of reducing radar signature.However,the curvature of the inlet usually causes different kinds of intake distortion at the aerodynamic interface plane(AIP).Among them,the swirl distortion has been seriously concerned because of its great impact on the performance and stability of aero-engines.There is still no universal criterion for assessing the stability of compressors in the condition of strong swirl distortion.As an approach of assessing the swirl intensity and pattern,vortex identification method may be used as an auxiliary method for stability analysis.In this paper,numerical and experimental investigations on different S-ducts were carried out.The axial vorticity component and g criterion were used to analyze the quantitative correlation between geometry and swirl intensity.It was found that there is a relatively strong correlation between the geometry,the axial vorticity component and the Q criterion.The present investigation may provide a quick reconstruction method to model the effect of S-ducts for compressor stability prediction.

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

ADAPTIVE HYBRID CARTESIAN GRID METHOD FOR VORTEX-DOMINATED FLOWS

An efficient compressible Euler equation solver for vortex-dominated flows is presented based on the adaptive hybrid Cartesian mesh and vortex identifying method.For most traditional grid-based Euler solvers,the excessive numerical dissipation is the great obstruction for vortex capturing or tracking problems.A vortex identifying method based on the curl of velocity is used to identify the vortex in flow field.Moreover,a dynamic adaptive mesh refinement(DAMR)process for hybrid Cartesian gird system is employed to track and preserve vortex.To validate the proposed method,a single compressible vortex convection flow is involved to test the accuracy and efficiency of DAMR process.Additionally,the vortex-dominated flow is investigated by the method.The obtained results are shown as a good agreement with the previous published data.

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

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.

Identification and analysis of the inlet vortex of an axial-flow pump

Axial-flow pumps are widely employed in urban flood control and drainage pumping stations.The inlet vortex is one factor that seriously threaten the safe,stable and efficient operation of axial-flow pump units.In this paper,the vortex recognition performances of two vortex identification methods,the Q—criterion and Liutex methods,are compared based on an axial-flow pump,and the interactions between the impeller and vortex are explored.A flat plate vortex generator is installed in front of the impeller to continuously induce a stable vortex.The numerical simulation results show that the Liutex method can not only simultaneously identify strong and weak vortices but also reduce the influence of shear force at the sidewall.The vortex and the impeller influence each other.Under the influence of rotating blades,the vortex changes from a low frequency to the blade frequency,and the vortex significantly changes the tangential velocity inside the impeller.The accuracy of the numerical simulation results is verified by experiments on the external and internal characteristics.

Liutex identification on hairpin vortex structures in a channel based on msfle and moving-PIV

The spatiotemporal evolution of hairpin vortex structures in a fully developed turbulent boundary layer is investigated qualitatively and quantitatively by using two image methods.In this paper,the moving single-frame and long-exposure(MSFLE)image method is used to intuitively track the evolution process of a hairpin vortex,while the moving particle image velocimetry(moving-PIV)method is applied for obtaining a moving velocity field for quantitative analysis.According to the structural characteristics of the hairpin vortex,an inclined light sheet with an appropriate inclination of 53°is arranged to capture the complete hairpin vortex structure at Re_(θ)=97–194.In addition,the core size and the rotational strength of a hairpin vortex are further defined and quantified by the Liutex vector method.The evolution process of a complete hairpin vortex structure observed by MSFLE shows that the shear along the normal direction leads to an increasing strength of the hairpin vortex,accompanied by a lifting vortex head and a distance decrease between two vortex legs during the dissipation period.By combining moving-PIV with the Liutex identification,the spatiotemporal evolution of four typical regions of a hairpin vortex projecting into a 53°cross-section is obtained.The results show that the process from the generation to the dissipation of a single hairpin vortex can be well characterized and recorded by the Liutex based on the core size and rotational intensity,and the evolution process is consistent with the MSFLE result.According to the statistics of vortex core size and rotation intensity along time,the evolution of the hairpin vortex necks and legs can be described as a process of enhancement followed by dissipation.For the vortex head,its evolution maintains longer attributed to its far-from-wall position,which consists of an absolute enhancement process(stage 1)with an increasing rotation strength and a constant core size,and an absolute dissipation(stage 2)with a decreasing rotation strength and a constant core size.

Evaluation of vortex evolution and energy loss within the impeller of a side channel pump

Side channel pumps can provide a huge pressure boost at very low specific speeds,making them useful in various industrial operations.Due to its very complex flow pattern,the high hydraulic head is often accompanied by lower efficiency and higher flow losses.In addition,the shape of the impeller has a direct influence on the flow pattern of the pump as well as the energy conversion that takes place,and this has a substantial bearing on the overall performance of the pump.Thus,to gain a deeper comprehension of the flow behavior and deep-seated reasons for performance optimization in side channel pumps with different geometry parameters.Extensive research has been conducted on the vortex formations and entropy production that occur inside the flow channels of the impeller.Three alternative impeller configurations were systematically created for in-depth research,each including a different suction angle for the blades.According to the data,the head of the side channel pump rises together with an increase in the suction angle,and this rule is exhibited in the whole working condition,and the most effective blade suction angle isθ=30°,which is the greatest of the available options.The vortex area and intensity have an obvious decrease when the suction angle increases to 30°,which is the main reason for the performance optimization.This paper firstly introduces the wall friction dissipation into the research on the side channel pump.Compared with turbulence dissipation and direct dissipation,the wall friction dissipation is far less than turbulence dissipation but far higher than direct dissipation that should not be neglected,although it also increases with the suction angle elevation.As the primary dissipation,the tendency of turbulence dissipation is upward with the performance increase,which is opposite to the common vane pump.The reason for this phenomenon is probably due to the deviation of the primary and secondary flow pattern in the side channel pump.As a result,this will assist to increase the performance and operational dependability of side channel pumps,which will ultimately lead to an expansion of the applications for these pumps.